Question

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

• A. $p=9,q=4$
• B. $p=9,q=6$
• C. $p=5,q=6$
• D. $p=4,q=9$

Answer 1

The correct option is A

$p=9,q=4$

$\text{In a parallelogram the diagonals bisect each other.}$

$\text{First diagonal is formed by the points (7,3) and (8,2)}$
$\text{The midpoint of this diagonal is}$

$(\frac{7+8}{2},\frac{3+2}{2})\equiv (\frac{15}{2},\frac{5}{2})$

$\text{Now, the other diagonal is formed by the points (6,1) and (p,q)}$

$\text{Midpoint of this diagonal =}$ $(\frac{6+p}{2},\frac{1+q}{2})$

$Hence,\frac{6+p}{2}=\frac{15}{2}$
$6+p=15$

$\Rightarrow p=9$

$Also,\frac{1+q}{2}=\frac{5}{2}$
$\Rightarrow 1+q=5$
$\Rightarrow q=4$