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

Answer 1

The correct option is D

p = 9, q = 4

The point of intersection of the diagonals bisect the diagonals in a parallelogram

First diagonal is formed by the points (7,3) and (8,2)
Point of intersection of the diagonals is the mid point of this diagonal

Hence, the point of intersection is $(\frac{7+8}{2},\frac{3+2}{2})$ = $(\frac{15}{2},\frac{5}{2})$

Now, the other diagonal is formed by the points (6,1) and (p,q)
The mid point of this diagonal is $(\frac{6+p}{2},\frac{1+q}{2})$

The point of intersection of the two diagonals is the same point

Hence, $\frac{6+p}{2}=\frac{15}{2}$
$6+p=15\Rightarrow p=9$

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