Question

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

• A. 0
• B. 3
• C. -2

Answer 1

The correct option is C -2

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