Question

If (7, 3), (6, 1), (8, 2) and (p, 4) are the vertices of a parallelogram taken in order, then find the value of p.

Answer 1

The midpoint of the diagonal AC and the diagonal BD coincide.

\((\frac{7+8}{2},\frac{3+2}{2})=(\frac{6+p}{2},\frac{1+4}{2})\)

\((\frac{15}{2},\frac{5}{2})=(\frac{6+p}{2},\frac{5}{2})\)

\(\frac{15}{2}=\frac{6+p}{2}\)

p = 9