Question

# Two adjacent vertices of a parallelogram are (3, 2) and (-1, 0) and the diagonals intersect at (2, -5). What are the other two vertices of the parallelogram?

A
(1, - 10), (5, - 10)
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B
(1, - 12), (5, - 10)
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C
(2, - 10), (5, - 12)
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D
(1, - 10), (2, - 12)
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Solution

## The correct option is B (1, - 12), (5, - 10)Let A and B be the given vertices and C be (x1,y1), D be (x2,y2) as shown below. Diagonals of a parallelogram bisect each other, so the midpoint of one diagonal will be the midpoint of the other. So, mid point (x, y) of the line joining the points (x1,y1) and (x2,y2) is given as x = (x1+x22) and y = (y1+y22) ∴ For the diagonal AC, x1+32=2 and y1+22=−5 ⇒x1=1 and y2=−12 ∴ Co-ordinates of C are (1, - 12) ∴ For the diagonal BD, x2−12=2 and y2+02=−5 ⇒x2=5 and y2=−10 ∴ Co-ordinates of D are (5, - 10)

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