Question

If two vertices of a parallelogram are (3, 2) and (-1, 0) and the diagonals interest at (2, -5), then the other two vertices are

• A. (1, - 10), (5, - 12)
• 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. since the diagonals of a parallelogram bisect each other



$\frac{x_1+3}{2}=2\Rightarrow x_1=1and\frac{y_1+2}{2}=-5\Rightarrow y_2=-12$
Co-ordinates of C are (1, - 12)

$\frac{x_2-1}{2}=2\Rightarrow x_2=5and\frac{y_2+0}{2}=-5\Rightarrow y_2=-10$
Co-ordinates of D are (5, - 10)