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# If the points A ( – 2, – 1), B (1, 0), C (p, 3) and D (1, q) form a parallelogram ABCD, find the values of p and q.

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An Important Question of M.L Aggarwal book of class 10 Based on Section Formula Chapter for ICSE BOARD.
If four points form a parallelogram then find the value aksed in the question inside that point.
This is the Question Number 24, Exercise 11 of M.L Aggarwal.

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### 1 Answer

1. Given vertices of the parallelogram are A(-2,-1), B(1, 0), C(p,3) and D(1,q).

Let M(x,y) be the midpoint of the diagonals of the parallelogram ABCD.

Diagonals AC and BD bisect each other at M.

When M is the midpoint of AC

By midpoint formula,

x = (-2+p)/2 = (p-2)/2 ..(i)

y = (-1+3)/2 = 2/2 = 1 ..(ii)

When M is the midpoint of BD

By midpoint formula,

x = (1+1)/2 = 2/2 = 1 ..(iii)

y = (q+0)/2 = q/2 ..(iv)

Equating (i) and (iii), we get

(p-2)/2 = 1

p-2 = 2

p = 2+2 = 4

Equating (i2) and (iv), we get

q/2 = 1

q = 2

Hence the value of p and q are 4 and 2 respectively.

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