Given the points ? (2, 9), ? (−3, 1) and ? (10, −2), Which of the

Question

Given the points 𝐴 (2, 9), 𝐵 (−3, 1) and 𝐶 (10, −2), Which of the following points could be the fourth vertex of parallelogram 𝐴𝐵𝐶𝐷?

A. (8,−11)
B. ( 5,8 )
C. (15,6 )
D. (5,−6) 
E. None of these.

Fdambro294 · Accepted Answer

For any parallelogram, the opposite sides must be both parallel and equal.

If you draw in the points and connect (-3 , 1) and (2 , 9) as one of the sides, follow the movements from the X coordinates and the Y coordinates

Then do those same movements from the end vertex (10, -2) ——this will ensure that both opposite side are parallel and congruent.

X coordinate: from -3 to 2——-> 5 units right along X axis

Y coordinate: from 1 to 9 ———-> 8 units up along the positive Y axis

Starting from vertex (10 , -2)

Moving 5 units right brings you to X coordinate = 15

Then moving 8 units up brings you to Y coordinate = 6

(15, 6)

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Kapil1650 · Answer

Distance between : -3,1 and 2,9 should be equal to 10,-2 and x,y
Solve x,y for all options . 
C fits in .

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giovannisumano · Answer

shouldn't the answer be D? if not please explain why

danbrown9445 · Answer

Opposite side should be parallel.
So AB || CD and both have same slope.
If (x1,y1) and (x2,y2) are 2 points on the same line then slope is given by (y2-y1)/(x2-x1)

Slope of AB = (1-9)/(-5) = 8/5
Slope of BC = (y+2)/(x-10) = 8/5

Looking at answer choices, substituting (15,6) for (x,y) satisfies the equation.

HWSVam · Answer

Since gmat worksheet is grided worksheet, can we just draw and work it out?

Usernamevisible · Answer

For parallelogram ABCD:
AB ∥ CD and BC ∥ AD
The naming order matters.
When a question says:
ABCD
it means the vertices are connected in order:
AB
BC
CD
DA
So in parallelogram ABCD:
AB ∥ CD
BC ∥ AD
NOT:
AC ∥ BD
because AC and BD are the diagonals.
A useful shortcut formula is:
D = A + C − B
Logic:
For parallelogram ABCD:
AB = DC
That means:
B − A = C − D
Rearrange:
D = A + C − B

Given:
A = (2, 9)
B = (−3, 1)
C = (10, −2)

Substitute:
D = (2, 9) + (10, −2) − (−3, 1)
= (2 + 10 + 3, 9 − 2 − 1)
= (15, 6)

Therefore, the fourth vertex is (15,6) - C

Given the points ? (2, 9), ? (−3, 1) and ? (10, −2), Which of the

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GMAT Problem Solving (PS) Questions

Given the points ? (2, 9), ? (−3, 1) and ? (10, −2), Which of the

Prep Toolkit

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