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.
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.
Updated On: Aug 18, 2024
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- 12
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The Correct Option is D
Solution and Explanation
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.
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