The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is
Explanation:
One of the diagonals of the parallelogram connects the points (2, 1) and (-3, -4).
Line x + 9y + c = 0, represents the other diagonal of the parallelogram.
We know, diagonals of a parallelogram bisect each other.
∴ x + 9y + c = 0 should pass through the midpoint of the line joining (2, 1) and (-3, -4).
The midpoint of the line joining (2, 1) and (-3, -4) = 2- 32,1 - 42 = (-0.5, -1.5)
⇒ Point (-0.5 , -1.5) lies on x + 9y + c = 0.
⇒ -0.5 + 9 × (-1.5) + c = 0
⇒ -0.5 - 13.5 + c = 0
⇒ c = 14.
Hence, option (d).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.