If the points A(2, 3), B(-5, 6), C(6, 7) and D(p, 4) are the vertices

If the points A(2, 3), B(-5, 6), C(6, 7) and D(p, 4) are the vertices of a parallelogram ABCD, find the value of p.

Answer

Mid point of AC = Mid point of BD

$$ \therefore \left(\frac{2 + 6}{2}, \frac{3 + 7}{2}\right) = \left(\frac{-5 + p}{2}, \frac{6 + 4}{2}\right) $$

$$ \frac{-5 + p}{2} = 4 \Rightarrow p = 13 $$