Question

The coordinates of the vertices of a parallelogram ABCD are A(x, y), B (5, 8), C (4, 7) and D (2, -4). Find the equation of diagonal BD.

• A. 8x-y-12=0
• B. 4x-y-12=0
• C. 4x-2y-12=0
• D. 4x-y-10=0

Answer 1

The correct option is B

4x-y-12=0

Equation of diagonal BD, using two point form of a line:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\Rightarrow y-8=\frac{-4-8}{2-5}(x-5)\Rightarrow y-8=\frac{-12}{-3}(x-5)\Rightarrow y-8=4(x-5)\Rightarrow y-8=4x-20\Rightarrow 4x-y-12=0$