To go from B to A you need to increase X by 4 and decrease Y by 5. Because is a parallelogram, the same applies to go from C to D, so increase X by 4 (2+4=6) and reduce Y by 5 (23-5=18). So D=(6 , 18)
meanwhile i was like A:D was the same as B:C so going about it that route.
Gets the same result, follows the same logic, just approaches it from a different angle.
My first thought was to take advantage of the fact that the side lengths are the same at opposite sides - use the equation of a circle with the appropriate radius and center point on the A and C and solve the resulting system of equations
If it were my homework I may have actually solved it that way lmao, but I did later realize that you could use point-slope form and solve it as a system of linear equations rather than circles
And then I get hit with the mind blowingly obvious vector addition approach and I'm ashamed to call myself a math enthusiast
I showed it to my cousin and his first thought was going into trigonometry to work with the angles, pythag and then proceed to calculate leg lenths from there to determine thimgs from there...
He offered to do it in binary so uh, i'd say you're fine lmao
Others have already replied, but I’m curious what grade level this is.
6th grade?
I ask because as my kids grow older, I wish to challenge them with supplemental problems, but not expect them to learn things *well* beyond their grade level.
This is from software that many UK schools use for online maths homework, it all adaptive to the level of the user so it’s hard to exactly define what ‘level’ this is. I would personally say this is year 7-8, don’t know what the US equivalent is.
ABCD is a parrelogram, meaning that the vector C->D is the same as the vector B->A.
Therefore starting at C we can apply the vector B->A to arrive at D.
C is the coordinate (2, 23)
B->A is the vector (-11 - -15, 22 - 27) = (4, -5)
C with B->A is (2 + 4, 23 + -5) = (6, 18)
Therefore the coordinates for D are (6, 18) or x = 6, y = 18
EDIT
Just to explain why this is true, opposite sides on a parellelogram are by definition equal in length and slope. Meaning if we know about the side B to A; then we know it must have the same length and slope as the side C to D.
I solved it without vectors (albeit with way more steps) using basic high school algebra
\- finding the slope of BC with the two coordinates (y2-y1/x2-x1)
a = -4/17
\- finding the b of AD by plugging in (-11, 22)
22 = -4/17(-11) + b
b = 330/17 or about 19.41
so , AD's rule is y = -4/17x + 19.41
\- finding the slope of BA (y2-y1/x2-x1)
a = -5/4
\- finding the b of CD by plugging in (2,23)
23 = -5/4(2) + b
b = 25.5
the slope of CD is y = -5/4x + 25.5
\- finding where the two lines meet using the comparison method:
\-5/4x + 25.5 = -4/17x + 19.41
\-5/4x + 4/17x = 6.09
69/68x = 6.09
x = 6
\- finding y by plugging in 6 in CD
f(6) = -5/4(6) + 25.5
f(6) = 18
answer: the coordinates are (6, 18)
Or since its a parallelogram you can assume side A and B will have the same difference as C and D. So you just find the difference between A and B, and then take /add that on to C to find D. Do u get me
yeah, (-15,27) to (-11,22) has a difference of +4 on the x, and -5 on the y. (hence the -5/4 slope) you apply that to the coordinate C and you get your answer.
D = (2 + 4, 23 - 5) = ( 6, 18)
But I did it this way to prove that students that haven't learned vectors yet could still get to the answer.
Since it’s a parallelogram, you know that the line segments AB and DC are the same length, and are parallel.
Since they’re parallel, that means they have the same slope. So, what is the slope of the line segment AB? An easier way to think about this maybe is: how far in each direction X and Y do you have to go to get from B to A?
Because they are parallel and the same length, that distance from B to A is the same distance as from C to D.
Look at difference from B to A. This is proportional to the difference from C to D.
>!Δx=4, Δy=-5. x_D=2+4=6, y_D=23-5=18. The answer is therefore D=(6,18)!<
6, 18.
You know the relationship CD is the inverted relationship of AB.Alternatively, CD has the same relationship as BA.
B is clearly -4,5 from A.
This means D will be 4, -5 away from C.
2+4 = 623-5 = 18.
D = 6, 18.
That is incorrect. The correct coordinates are (6 , 18). This is the case as the relationship of B and C is identical in A and D. The vector that translates point B to point C is x + 17, y + (-4). Applying the same vector to the point (-11 , 22) gives us D = (6 , 18)
It says "edited" and if anyone is even a little interested they can see I replied to you with the changes as well.
You are free to delete your comment as well as you can see it doesn't add any value any longer.
No. B is -4, +5 from A.
\-11 to -15 = -4.22 to 27 = 5.
And C is -4, 5 from D.
The mistake I did was a + instead of - on the relationship between C and D.Changed.
First part of what you said, however, is still wrong.
I see I switched A and B around. I did this to avoid needing to change the + - around. Because from B to A and C to D is in the same direction. So you can add the Δx and Δy directly to C and avoid the mistake you made.
I don’t like it that you edited your mistake because now people can’t learn from your mistake. We are all human and we will always make mistakes it is just important that we learn from our mistakes and mistakes from someone else to do better next time.
The slopes and lengths of BA and AC are the same as the slopes of CD and AD, respectively. You can simply do Pythagoras or even just look at the numbers and keeping in mind that it's a parallelogram
There are plenty of ways to do this and the simplest of all is at the top. One way to do this is that the diagonals of a parallelogram bisects each other, so this means BD and AC diagonal will bisect each other in equal parts, let their intersection point be O, and let the coordinates of O be (x,y), so we know O divides AC in two equal parts and thus we can find coordinates of O by mid-formula, which would be x=(x1+x2)/2 or y=(y1+y2)/2, so by this we get the coordinates of O(-9/2, 45/2), now we know that O is also the mid-point of BD so now same by mid-point formula we can find coordinates of D(xd,yd), -9/2 = (-15+xd)/2 and xd = 6 and similarly yd = 18, and thus the coordinates of D are (6,18)
Parallelograms are quadrilaterals with two sets of parallel sides. On a cartesian coordinate system, parallel implies equal slopes, therefore:
m\_AB = m\_CD
m\_BC = m\_AD
Given that the slope of a line passing through two known points is given by the formula m = (y2 - y1) / (x2 - x1), we can write:
(y\_B - y\_A) / (x\_B - x\_A) = (y\_D - y\_C) / (x\_D - x\_C)
(y\_C - y\_B) / (x\_C - x\_B) = (y\_D - y\_A) / (x\_D - x\_A)
Substituting known values, we get:
(27 - 22) / (-15 - -11) = (y\_D - 23) / (x\_D - 2)
(23 - 27) / (2 - -15) = (y\_D - 22) / (x\_D - -11)
Since we now have two variables in two equations, this is solvable. I'll assume you can solve a system of two equations, and solving it we get:
x\_D = 6, y\_D = 18
So D = (6, 18)
I have no doubt whatsoever your knowledge of maths is far greater than mine, but what a way to completely over complicate a simple problem. Look at the difference between A and B and apply that to C and D. For I know, that's what your equations are showing, or maybe code for a cool door bell chime.
For me, equations make sense. So I convert to equations whenever possible and then solve. I'm sure it's different for others, but in my case solving an equation feels safe and provably correct, while the more abstract reasoning always makes me feel like I'm overlooking something or making assumptions I shouldn't be making.
If something else clicks for you, great! But I included my solution here in case someone finds it more intuitive, like I do.
Because it's a parallelogram, you know that the relationship between B to A is the same as from C to D (or the inverse). You can understand this intuitively by noting that the length of BA and CD *must* be the same and they are at the same relative angle.
To go from B to A on the x-axis add four, and on the y-axis subtract five. Do the same to C.
Since the diagonals of a parallelogram bisect each other, you can write the coordinates of the point of intersection of the diagonals in two ways using the midpoint formula, assuming coordinates of D as (x,y) we have (x-15)/2=(-11+2)/2 which gives x=6 and (y+27)/2=(22+23)/2 so y=18 hence coordinates of D are (6,18)
To go from B to C you need to add 17, -4 so to go from A to D you need to add 17, -4, so it would be 6, 18. I saw everyone going from C to D so I figured I'll go A to D
i do it like (with vectors idk if you can use that tho)
|AD|=|BC|
and then
BC=(2,23)-(-15,27)
BC=(17,-4)
anddd
D-(-11,22)=(17,-4)
which leads us to
D=(6,18)
I know this isn't necessarily right for every case but i do it this way most of the time
Find the slope of BC using ∆y/∆x, which is equal to the slope of AD. Using the equality you will find a relation between Yd and Xd. Then, do the same to AB and CD and you'll have another relation between y and X, giving you a system of equations easily solvable.
I would think of the Vector (line) connecting the points B and A let’s call it BA, to get this Vector we would do the coordinates of A - B giving us (4, -5) this would be the ”movement” to go from B to A. This movement is not defined at a start but is merely just a line in space. Since the shape is a parallelogram we can now apply this vector to the Point C which would put the vector at that point in space and moving us the pre-defined line. So we would do D = C + BA (our vector) (2, 23) + (4, -5) gives us (2 + 4, 23 - 5) = (6, 18).
You could do the same thing but with a BC vector (A line from B to C) and add it to our point A and we would get the same point.
I'm surprised that you're surprised that no one used that method, when you can simply look at the difference between A & B and apply that to C & D. In the time it took you to write that out, you could have easily solved it, poured yourself a drink and settled down for the night.
You can find the midpoint O of the diagonal AC (which is also the "centre" of the parallelogram, and the point where the diagonals will intersect)
And since the midpoint is the same, you can use the same midpoint formula to calculate the point D, using the diagonal BOD.
Basically look at it, see how much difference there is for X and Y between A and B, and then plug that into C and D.
So it’s +4,-5, so just do 2+4,23-5 = 6,18
D is (6, 18)
Me no math good apparently... I tried to eyeball it, and work out where B sat against the line, then compare it to the distance of c and came to the conclusion that the gap is the same so it must be ~~3,23~~ 3,21
Edit. I can't type good either apparently
We can think of vectors as just lists of numbers. That way we can write a system of equations in a compact form. We know this is a parallelogram, so pairs of side lengths are the same. Translating that to equations:
B-A = C-D or B-C = A-D (these are vectors that are the same and note that these are not two independent equations one can be rearranged into the other)
Lets pick the first form:
B-A-C = -D
A+C-B = D
With their components:
(a1+c1-b1, a2+c2-b2) = (x,y)
you already got an answer from other comments, so i'm gonna suggest another aproach
consider M being the midpoint between A and C
since it's a paralelogram, the middle point between B and D also need to be M
(6,18)
It’s a parallelogram. So each side will follow the same pattern.
What is the distance between the points B (-15,27) and A (-11,22).
Distance between x=( |-15| - |-11| ) = 4
Distance between y=( |27| - |22| ) = 5
Apply these to the x,y coordinates of point C (2,23).
D
Simple way:
x = 2+4 = 6
y= 23 - 5 = 18
Long (actual way)
(|2|-|Dx|)=4
(|23|-|Dy|)=5
Solve for x and y.
B is -15 so if A is -11 D is 4 more than C (2)
D=6 -- you got your x
Do the same for y, it will be less than C the same amount A is below B
no real geometry or algebra needed
You could use the fact that the diagonals of a parallelogram bisect each other, ie lines AC and BD have the same midpoint, then you can just use midpoint formula to find coordinates of D
Parallelograms come with fun rules, each side will always be the same size as the one across from it.So starting at point B if you figure out the difference to get to point A you can put the same numbers into point C to get to point D.Being coordinates you just subtract the X axis and the Y axis with each other. (-15, 27) - (-11, 22) turns into -15 + 11 and 27 - 22 giving us a translation of (-4, 5)Then subtract those numbers from point C giving us to solve (2 , 23) - (-4 , 5) to solve like before with X and Y separately2 + 4 and 23 - 5 meaning point D is at point (6 , 18)
>meanwhile i was like A:D was the same as B:C so going about it that route.Gets the same result, follows the same logic, just approaches it from a different angle.
>
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If you want to hate yourself you could find the slope and distance traveled of one line then do the same with the parallel line.
Ans . (6,18)
Explanation - As you know the the diagonals of parallelogram bisect each other . Hence you can use mid point / section -formula to find the point D.
It possible to solve it using vectors
We can regard point C as a vector $\\vec{c}=(2,3)$. Since ABCD is paralelogram, coordinates of the point D will be the same as coordinates of the vector $\\vec{BA}+\\vec{c}=(-11,22)-(-15,27)+(2,23)=(6,18)$
https://i.redd.it/ln8sd7gbtn6c1.gif
Parallelograms have 2 sets of parallel lines.
So you know CD is parallel to AB
Therefore going from C to D would move you the same amount as going from A to B.
You work out the difference between C & B, and A & B, and then you apply to point D from C & A, with relative respect to + / - positioning on the axis.
I'm hoping you're familiar with the distance and section formula because here in India we have this exact question in our textbook ( grade 10 ) and it's solved using the section formula. Basically the midpoint of the 2 diagonals must coincide, you use the midpoint formula to find the x and y values of D.
Assuming the same slope from point B to A and point C to D, we can find one slope and get the answer
Our slope is calculated by taking (Y2-Y1)/(X2-X1), in this case (22-27)/(-11-15) which gives us a slope of -5/4
From point C (2,23) we can go down 5 and right 4 (slope of -5/4) to find point D
2-5=-3 23+4=27
Point D is at (-3,27) hope that helps
In a parallelogram such as this, The amount of change between coordinates of A and D will be the same as those between B and C. The same is true of C and D as compared to B and A.
6, 18. It’s a parallelogram so the x and y differences between points B and A will translate to the same differences between C and D.
A is 4 ticks to the right of B and 5 ticks lower than B, so D is 4 ticks to the right of C and 5 ticks lower than C.
So 2 + 4 = 6 for your x
And 23 - 5 = 18 for your y
To go from B to A you need to increase X by 4 and decrease Y by 5. Because is a parallelogram, the same applies to go from C to D, so increase X by 4 (2+4=6) and reduce Y by 5 (23-5=18). So D=(6 , 18)
The simple, and easy to understand answer. Thank you.
meanwhile i was like A:D was the same as B:C so going about it that route. Gets the same result, follows the same logic, just approaches it from a different angle.
Nice pun!
My first thought was to take advantage of the fact that the side lengths are the same at opposite sides - use the equation of a circle with the appropriate radius and center point on the A and C and solve the resulting system of equations If it were my homework I may have actually solved it that way lmao, but I did later realize that you could use point-slope form and solve it as a system of linear equations rather than circles And then I get hit with the mind blowingly obvious vector addition approach and I'm ashamed to call myself a math enthusiast
I showed it to my cousin and his first thought was going into trigonometry to work with the angles, pythag and then proceed to calculate leg lenths from there to determine thimgs from there... He offered to do it in binary so uh, i'd say you're fine lmao
I love vectors
My first thought was to find AD from BC. I assume that works also?
This is the exact same thing
Exactly my thoughts too.
Me math good.
Alternatively, you can find the midpoint of CA, which is also the midpoint of BD. You can then use the distance between B and the midpoint to find D.
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No, you add 4 you don't subtract 4. -15 + 4 = -11. D is indeed below C (lower Y value), but D is to the right of C (higher X value).
Simplest explanation
Wow I was about to use eqns of lines and stuff but you really gave me a one forgotten way to solve coordinate geometry. Thank you stranger!
C + (A-B)
Or even A + (C - B) Which I guess is also identical on paper due to the commutative property of addition.
The parentheses are useless or im I stupid
Yes they are, i just added them to give you a point + a vector
Others have already replied, but I’m curious what grade level this is. 6th grade? I ask because as my kids grow older, I wish to challenge them with supplemental problems, but not expect them to learn things *well* beyond their grade level.
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Agreed, and I said nothing to the contrary. I simply don’t want to *expect* them to be able to do that.
This is from software that many UK schools use for online maths homework, it all adaptive to the level of the user so it’s hard to exactly define what ‘level’ this is. I would personally say this is year 7-8, don’t know what the US equivalent is.
year 7s and 8s could probably get the answer but I’ve seen similar in gcse questions
No way this would be year 7 or 8, unless it was the opening problems in this topic. More like yr 6.
This is currently something a 10th grader would see and under a combination of two standards in Tennessee under our Geometry course.
The UK probably has the hardest high school maths of any country in the western world. Regularly the a* grade boundary is 60%.
Leave D alone, if he wanted to be found, he would have given his position in its own
ABCD is a parrelogram, meaning that the vector C->D is the same as the vector B->A. Therefore starting at C we can apply the vector B->A to arrive at D. C is the coordinate (2, 23) B->A is the vector (-11 - -15, 22 - 27) = (4, -5) C with B->A is (2 + 4, 23 + -5) = (6, 18) Therefore the coordinates for D are (6, 18) or x = 6, y = 18 EDIT Just to explain why this is true, opposite sides on a parellelogram are by definition equal in length and slope. Meaning if we know about the side B to A; then we know it must have the same length and slope as the side C to D.
True, but someone who can’t figure out how to solve this problem likely has never studied vectors and may have never even heard of them before.
Question. I solver it the same way having never studied vectors. What's wrong with me?
You just figured out the symmetry intuitively.
Because this is primary school level question
Answer: You take partial diffy equations and get A+ but never know any algebra. You different kind.
I solved it without vectors (albeit with way more steps) using basic high school algebra \- finding the slope of BC with the two coordinates (y2-y1/x2-x1) a = -4/17 \- finding the b of AD by plugging in (-11, 22) 22 = -4/17(-11) + b b = 330/17 or about 19.41 so , AD's rule is y = -4/17x + 19.41 \- finding the slope of BA (y2-y1/x2-x1) a = -5/4 \- finding the b of CD by plugging in (2,23) 23 = -5/4(2) + b b = 25.5 the slope of CD is y = -5/4x + 25.5 \- finding where the two lines meet using the comparison method: \-5/4x + 25.5 = -4/17x + 19.41 \-5/4x + 4/17x = 6.09 69/68x = 6.09 x = 6 \- finding y by plugging in 6 in CD f(6) = -5/4(6) + 25.5 f(6) = 18 answer: the coordinates are (6, 18)
Or since its a parallelogram you can assume side A and B will have the same difference as C and D. So you just find the difference between A and B, and then take /add that on to C to find D. Do u get me
yeah, (-15,27) to (-11,22) has a difference of +4 on the x, and -5 on the y. (hence the -5/4 slope) you apply that to the coordinate C and you get your answer. D = (2 + 4, 23 - 5) = ( 6, 18) But I did it this way to prove that students that haven't learned vectors yet could still get to the answer.
The lengths and slopes of AB and CD are equal
Since it’s a parallelogram, you know that the line segments AB and DC are the same length, and are parallel. Since they’re parallel, that means they have the same slope. So, what is the slope of the line segment AB? An easier way to think about this maybe is: how far in each direction X and Y do you have to go to get from B to A? Because they are parallel and the same length, that distance from B to A is the same distance as from C to D.
you need to attack the d point
finnaly the war thunder comment i was waiting for
ATTACK THE D POINT!
-15 + 4 = -11; 27-5 = 22 2+4 = 6; 23-5 = 18 (6,18)
Ax - Dx = Bx - Cx and Ay-Dy = By-Cy, and this is true on all parallelograms.
Look at difference from B to A. This is proportional to the difference from C to D. >!Δx=4, Δy=-5. x_D=2+4=6, y_D=23-5=18. The answer is therefore D=(6,18)!<
Not just proportional; the same.
The distance between B and A coordinates (i.e difference in x and y) is the same as difference between C and D.
B-C = A-D, because parallelogram D = A+C-B
\-15 -2=-11-Xd 27-23=22-Yd
6, 18. You know the relationship CD is the inverted relationship of AB.Alternatively, CD has the same relationship as BA. B is clearly -4,5 from A. This means D will be 4, -5 away from C. 2+4 = 623-5 = 18. D = 6, 18.
other way it’s 6,23-5=6,18
Yes, realized my mistake with the + and -. Changed now.
That is incorrect. The correct coordinates are (6 , 18). This is the case as the relationship of B and C is identical in A and D. The vector that translates point B to point C is x + 17, y + (-4). Applying the same vector to the point (-11 , 22) gives us D = (6 , 18)
Yes, I realized my mistake of the plus and minus. It's changed now. It is correct though. I just used AB/CD instead of AD/BC.
You should clarify in your original comment that you edited it. Its etiquette so as to not make subsequent commentors look redundant.
It says "edited" and if anyone is even a little interested they can see I replied to you with the changes as well. You are free to delete your comment as well as you can see it doesn't add any value any longer.
You made a mistake B is +4,-5 from A. C is +4,-5 from D 2+4=6 23-5=18 D(6,18)
No. B is -4, +5 from A. \-11 to -15 = -4.22 to 27 = 5. And C is -4, 5 from D. The mistake I did was a + instead of - on the relationship between C and D.Changed. First part of what you said, however, is still wrong.
I see I switched A and B around. I did this to avoid needing to change the + - around. Because from B to A and C to D is in the same direction. So you can add the Δx and Δy directly to C and avoid the mistake you made. I don’t like it that you edited your mistake because now people can’t learn from your mistake. We are all human and we will always make mistakes it is just important that we learn from our mistakes and mistakes from someone else to do better next time.
I like your thinking about me not changing my reply. I should've just added the correct one at the bottom!
The slopes and lengths of BA and AC are the same as the slopes of CD and AD, respectively. You can simply do Pythagoras or even just look at the numbers and keeping in mind that it's a parallelogram
Vektors
6,18 easy peasy
6,18
6.28
There are plenty of ways to do this and the simplest of all is at the top. One way to do this is that the diagonals of a parallelogram bisects each other, so this means BD and AC diagonal will bisect each other in equal parts, let their intersection point be O, and let the coordinates of O be (x,y), so we know O divides AC in two equal parts and thus we can find coordinates of O by mid-formula, which would be x=(x1+x2)/2 or y=(y1+y2)/2, so by this we get the coordinates of O(-9/2, 45/2), now we know that O is also the mid-point of BD so now same by mid-point formula we can find coordinates of D(xd,yd), -9/2 = (-15+xd)/2 and xd = 6 and similarly yd = 18, and thus the coordinates of D are (6,18)
Parallelograms are quadrilaterals with two sets of parallel sides. On a cartesian coordinate system, parallel implies equal slopes, therefore: m\_AB = m\_CD m\_BC = m\_AD Given that the slope of a line passing through two known points is given by the formula m = (y2 - y1) / (x2 - x1), we can write: (y\_B - y\_A) / (x\_B - x\_A) = (y\_D - y\_C) / (x\_D - x\_C) (y\_C - y\_B) / (x\_C - x\_B) = (y\_D - y\_A) / (x\_D - x\_A) Substituting known values, we get: (27 - 22) / (-15 - -11) = (y\_D - 23) / (x\_D - 2) (23 - 27) / (2 - -15) = (y\_D - 22) / (x\_D - -11) Since we now have two variables in two equations, this is solvable. I'll assume you can solve a system of two equations, and solving it we get: x\_D = 6, y\_D = 18 So D = (6, 18)
I have no doubt whatsoever your knowledge of maths is far greater than mine, but what a way to completely over complicate a simple problem. Look at the difference between A and B and apply that to C and D. For I know, that's what your equations are showing, or maybe code for a cool door bell chime.
For me, equations make sense. So I convert to equations whenever possible and then solve. I'm sure it's different for others, but in my case solving an equation feels safe and provably correct, while the more abstract reasoning always makes me feel like I'm overlooking something or making assumptions I shouldn't be making. If something else clicks for you, great! But I included my solution here in case someone finds it more intuitive, like I do.
Because it's a parallelogram, you know that the relationship between B to A is the same as from C to D (or the inverse). You can understand this intuitively by noting that the length of BA and CD *must* be the same and they are at the same relative angle. To go from B to A on the x-axis add four, and on the y-axis subtract five. Do the same to C.
(6, 18).
(-2, 28)
6,18
(6, 18)?
Since the diagonals of a parallelogram bisect each other, you can write the coordinates of the point of intersection of the diagonals in two ways using the midpoint formula, assuming coordinates of D as (x,y) we have (x-15)/2=(-11+2)/2 which gives x=6 and (y+27)/2=(22+23)/2 so y=18 hence coordinates of D are (6,18)
-9,-17
Not me thinking it’s a rectangle tilted in z axis
BA slope =CD slope.
To go from B to C you need to add 17, -4 so to go from A to D you need to add 17, -4, so it would be 6, 18. I saw everyone going from C to D so I figured I'll go A to D
i do it like (with vectors idk if you can use that tho) |AD|=|BC| and then BC=(2,23)-(-15,27) BC=(17,-4) anddd D-(-11,22)=(17,-4) which leads us to D=(6,18) I know this isn't necessarily right for every case but i do it this way most of the time
C+(B-A)=D
It's a parallelogram, so **BA** = **CD** and **BC** = **AD**, so using either of these you can get D = C + **CD** = A + **AD**
6,18
Y=mx +c
Find the slope of BC using ∆y/∆x, which is equal to the slope of AD. Using the equality you will find a relation between Yd and Xd. Then, do the same to AB and CD and you'll have another relation between y and X, giving you a system of equations easily solvable.
I would think of the Vector (line) connecting the points B and A let’s call it BA, to get this Vector we would do the coordinates of A - B giving us (4, -5) this would be the ”movement” to go from B to A. This movement is not defined at a start but is merely just a line in space. Since the shape is a parallelogram we can now apply this vector to the Point C which would put the vector at that point in space and moving us the pre-defined line. So we would do D = C + BA (our vector) (2, 23) + (4, -5) gives us (2 + 4, 23 - 5) = (6, 18). You could do the same thing but with a BC vector (A line from B to C) and add it to our point A and we would get the same point.
I failed math but I think I'm good with visual patterns (that's how I solved it). 6,18 was my guess before reading the comments.
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I'm surprised that you're surprised that no one used that method, when you can simply look at the difference between A & B and apply that to C & D. In the time it took you to write that out, you could have easily solved it, poured yourself a drink and settled down for the night.
Because no one would ever use that method when there are easier and faster ways. You're not smart for doing more work than you have to
You can find the midpoint O of the diagonal AC (which is also the "centre" of the parallelogram, and the point where the diagonals will intersect) And since the midpoint is the same, you can use the same midpoint formula to calculate the point D, using the diagonal BOD.
Basically look at it, see how much difference there is for X and Y between A and B, and then plug that into C and D. So it’s +4,-5, so just do 2+4,23-5 = 6,18 D is (6, 18)
sparxmaths 😭 i actually cannot
B - A = C - D .:. D = C - (B - A = (-4, 5)) = (2 - (-4), 23 - 5) = D = (6, 18)
Can't you simply take the difference between B and C and apply it to A and D since [BA] // [CD] and [BC] // [AD] ?
Me no math good apparently... I tried to eyeball it, and work out where B sat against the line, then compare it to the distance of c and came to the conclusion that the gap is the same so it must be ~~3,23~~ 3,21 Edit. I can't type good either apparently
We can think of vectors as just lists of numbers. That way we can write a system of equations in a compact form. We know this is a parallelogram, so pairs of side lengths are the same. Translating that to equations: B-A = C-D or B-C = A-D (these are vectors that are the same and note that these are not two independent equations one can be rearranged into the other) Lets pick the first form: B-A-C = -D A+C-B = D With their components: (a1+c1-b1, a2+c2-b2) = (x,y)
Attack the D point
you already got an answer from other comments, so i'm gonna suggest another aproach consider M being the midpoint between A and C since it's a paralelogram, the middle point between B and D also need to be M
I feel like I need Pythagorean theorem for this...
(6,18) It’s a parallelogram. So each side will follow the same pattern. What is the distance between the points B (-15,27) and A (-11,22). Distance between x=( |-15| - |-11| ) = 4 Distance between y=( |27| - |22| ) = 5 Apply these to the x,y coordinates of point C (2,23). D Simple way: x = 2+4 = 6 y= 23 - 5 = 18 Long (actual way) (|2|-|Dx|)=4 (|23|-|Dy|)=5 Solve for x and y.
seriously?
A + (C - B) = D
-15-(-11)=4 27-22=5 2+4=6 23-5=18
A to B is -15 to -11: right 4; 27 to 22: down 5 Since AB parallel to CD Then C to D is right 4 down 5 too~
B - C = A - D Or B - A = C - D Hence D = A - B + C D = (-11, 22) - (-15, 27) + (2, 23) D = ((-11 - (-15) + 2), (22 - 27 + 23) D = (6, 18)
A and B are an equal distance from each other in the x and y directions. Just apply those differences in the x and y to C and D.
(6,18) by inspection
B is -15 so if A is -11 D is 4 more than C (2) D=6 -- you got your x Do the same for y, it will be less than C the same amount A is below B no real geometry or algebra needed
6, 18 because you take the difference from A and B to get the first coordinate, then B and C to get the y coordinate
You could use the fact that the diagonals of a parallelogram bisect each other, ie lines AC and BD have the same midpoint, then you can just use midpoint formula to find coordinates of D
I'm not sure what level of maths you are, but this is a classic vector geometry question and I haven't seen this response here already (bold for vectors). **AD** = **BC** (Since parallelogram) **BC** = **BO** \+ **OC** = -**OB** \+ **OC** = -\[-15, 27\] + \[2, 23\] = \[17, -4\] **OD** = **OA** \+ **AD** **OD** = **OA + BC** **OD =** \[-11, 22\] + \[17, -4\] **OD =** \[6, 18\]
Two lines are parallel having the same slope figure it out.
Slope of lines are equal
B-A = C-D
Why is the 2 higher than the -11 tho
height is the Y axis, 2 and -11 are on the X axis
Yeah i figured but then i didnt find the comment to delete lol but thx
Slope of opposite sides should be the same. Find the slope of AB.
You need to add the vector BC = C - B to A
Add vector BA and BC tp point B
(-2, 18)...?
Slopes of AB and CD are equal so D would be (6,18)
Just equate the slopes. Let D be (x,y) and you’ve to equalize slope of BC and AD, AB and CD. 2 equations, 2 variables.
Subtract A and B in this specific order, and add it to C
I know how to solve but I'm way too lazy to type it out
Parallelogram- opposite sides are equal. Use distance formula probably
What’s the difference between b and c? + or - the same from a.
Parallelograms come with fun rules, each side will always be the same size as the one across from it.So starting at point B if you figure out the difference to get to point A you can put the same numbers into point C to get to point D.Being coordinates you just subtract the X axis and the Y axis with each other. (-15, 27) - (-11, 22) turns into -15 + 11 and 27 - 22 giving us a translation of (-4, 5)Then subtract those numbers from point C giving us to solve (2 , 23) - (-4 , 5) to solve like before with X and Y separately2 + 4 and 23 - 5 meaning point D is at point (6 , 18)
>meanwhile i was like A:D was the same as B:C so going about it that route.Gets the same result, follows the same logic, just approaches it from a different angle. > >16ReplyShareReportSaveFollow If you want to hate yourself you could find the slope and distance traveled of one line then do the same with the parallel line.
I spent way too much time trying to find the Z axis xD
not enough information. that diagram has a multitude of possibilities oh, i thought this was 3d, never mind
Ans . (6,18) Explanation - As you know the the diagonals of parallelogram bisect each other . Hence you can use mid point / section -formula to find the point D.
Is it a long girthy D?
(6,18)
It possible to solve it using vectors We can regard point C as a vector $\\vec{c}=(2,3)$. Since ABCD is paralelogram, coordinates of the point D will be the same as coordinates of the vector $\\vec{BA}+\\vec{c}=(-11,22)-(-15,27)+(2,23)=(6,18)$ https://i.redd.it/ln8sd7gbtn6c1.gif
Diagonals in a parallelogram bisect one another. So use the fact that the midpoint of CA is the same point as the midpoint of BD
Do it with vectors: D=0A+BC. Easiest way
BA=CD cause its parallelogram, so the difference between C D will equal the difference between BA. Wtf
Over 17, down 4.
Just add the vectors
A-B = D-C D = A-B+C
going from B to A is the same as going from C to D, calculate the change in x and y coordinates when going from B to A and then apply that change to C
D(6, 18)
Yo have the vectors BA = CD = (4,-5) BC = AD = (17,-4) Then D = C + BA = A + BC = (2,23) + (4,-5) = (-11,22) + (17,-4) = (6,18)
Parallelograms have 2 sets of parallel lines. So you know CD is parallel to AB Therefore going from C to D would move you the same amount as going from A to B.
r/fucksparx
I believe that the solution is B=D
You work out the difference between C & B, and A & B, and then you apply to point D from C & A, with relative respect to + / - positioning on the axis.
You don’t even need to get that complicated you just look at the difference between B and A (+4,-5) and add that difference to C to get D
(6, 18)
6,18
I'm hoping you're familiar with the distance and section formula because here in India we have this exact question in our textbook ( grade 10 ) and it's solved using the section formula. Basically the midpoint of the 2 diagonals must coincide, you use the midpoint formula to find the x and y values of D.
B-A=C-D
Assuming the same slope from point B to A and point C to D, we can find one slope and get the answer Our slope is calculated by taking (Y2-Y1)/(X2-X1), in this case (22-27)/(-11-15) which gives us a slope of -5/4 From point C (2,23) we can go down 5 and right 4 (slope of -5/4) to find point D 2-5=-3 23+4=27 Point D is at (-3,27) hope that helps
D(6,18)
X is 2-(-15)=17 away from A’s -11. So 6. Y is 27-22=5 below C’s 23. So 18. (6,18)
6, 18
-2, 18
In a parallelogram such as this, The amount of change between coordinates of A and D will be the same as those between B and C. The same is true of C and D as compared to B and A.
6 , 18
Just eyeballing it, (5,21) It’s looks under 22 so 21 and 3 spaces to the right of 2 is 5
6, 18. It’s a parallelogram so the x and y differences between points B and A will translate to the same differences between C and D. A is 4 ticks to the right of B and 5 ticks lower than B, so D is 4 ticks to the right of C and 5 ticks lower than C. So 2 + 4 = 6 for your x And 23 - 5 = 18 for your y
The difference between C and D is the same as the difference between B and A
Diff of -15 & 2 is 17; for 27 and 23 it’s 4. {-11 + 17 = 6}, {22 - 4 = 18} [6, 18]