Question

Two adjacent vertices of a parallelogram are (3, 2) and (-1, 0) and the diagonals intersect at (2, -5). What are the other two vertices of the parallelogram?

• A. (1, - 10), (5, - 10)
• B. (1, - 12), (5, - 10)
• C. (2, - 10), (5, - 12)
• D. (1, - 10), (2, - 12)

Answer 1

The correct option is B (1, - 12), (5, - 10)

Let A and B be the given vertices and C be $(x_1,y_1)$, D be $(x_2,y_2)$ as shown below.

Diagonals of a parallelogram bisect each other, so the midpoint of one diagonal will be the midpoint of the other.
So, mid point (x, y) of the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is given as x = $\left(\frac{x_1+x_2}{2}\right)$ and y = $\left(\frac{y_1+y_2}{2}\right)$

$\therefore$ For the diagonal AC, $\frac{x_1+3}{2}=2\text{and}\frac{y_1+2}{2}=-5$
$\Rightarrow x_1=1\text{and}{y}_2=-12$
$\therefore$ Co-ordinates of C are (1, - 12)

$\therefore$ For the diagonal BD,
$\frac{x_2-1}{2}=2\text{and}\frac{y_2+0}{2}=-5$
$\Rightarrow x_2=5\text{and}{y}_2=-10$
$\therefore$ Co-ordinates of D are (5, - 10)