Question

If the points A(1, 2), B(4, 3), C(1, 0) and D(p, -1) are the vertices of a parallelogram then, find the value of p.

• A. 3
• B. -2
• C. 4

Answer 1

The correct option is B -2

In a parallelogram, the diagonals bisect each other.

So the midpoints of both the diagonals will coincide.

Midpoint of AC = Midpoint of BD

$(\frac{1+1}{2},\frac{2+0}{2})=(\frac{4+p}{2},\frac{3-1}{2})$

$\Rightarrow (1,1)=(\frac{4+p}{2},1)$

$\Rightarrow 1=\frac{4+p}{2}$

$\Rightarrow p=-2$