Question

The points (–4, 3) and (–1, –4) are two end points of a diagonal of a parallelogram. If the other diagonal has the equation 7y + 3x + c = 0, then find the value of c.

• A. 8
• B. 9
• C. 10
• D. 11
• E. 12

Answer 1

Answer: (D)

11

Answer 2

For any parallelogram, the diagonals bisect each other.

The midpoint of $(–4, 3)$ and $(–1, –4)$ will also lie on $7y + 3x + c = 0$.

The midpoint of $(–4, 3)$ and $(–1, –4)$ is $\bigg(\frac{-4-1}{2}, \frac{3+(-4)}{2}\bigg)$ = $(-2.5, -0.5)$.

On substituting in the equation, we get $7(-0.5) +3(-2.5) +c = 0$

$c = 11$

Hence, option D is the correct answer.