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

The Correct Option is D

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.