Question

If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram taken in order Then the value of P is

• A. 7
• B. 8
• C. 4
• D. 9

Answer 1

Answer: (A)

7

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 $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
So, midpoint of $AC=$ Mid point of $BD$
$=>(\frac{6+9}{2},\frac{1+4}{2})=(\frac{8+P}{2},\frac{2+3}{2})$
$=>(\frac{15}{2},\frac{5}{2})=(\frac{8+P}{2},\frac{5}{2})$
$=>8+P=15$
$=>P=7$