Question

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

• A. 3
• B. -2
• C. 4
• D. 0

Answer 1

The correct option is B

-2

In a parallelogram, the diagonals bisect each other.
So the midpoints of both the diagonals coincide.
Midpoint of AC = Midpoint of BD
$i.e.(\frac{1+1}{2},\frac{2+0}{2})=(\frac{4+p}{2},\frac{3-1}{2})\Rightarrow (\frac{2}{2},\frac{2}{2})=(\frac{4+p}{2},\frac{2}{2})\Rightarrow 1=\frac{4+p}{2}\Rightarrow p=-2$