Question

If (7, 3), (6, 1), (8, 2) and (P, 4) are the vertices of a parallelogram taken in order then the value of P is :

• A. 4
• B. 6
• C. 7
• D. 9

Answer 1

The correct option is D 9

Let $A(7,3),B(6,1),C(8,2)$ and $D(P,4)$
We know that the diagonals of a parallelogram bisect each other. So,the midpoint of AC is same as the mid point of BD.
Mid point of two points ${(x}_1,y_1)$ and ${(x}_2,y_2)$ is calculated by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
$=>(\frac{7+8}{2},\frac{3+2}{2})=(\frac{6+p}{2},\frac{1+4}{2})$
$=>\frac{7+8}{2}=\frac{6+p}{2}$
$=>15=6+p$
$=>p=9$