CAT 2020 Slot 3 QA Question 8: 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

Question

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

Accepted Answer

In a parallelogram, the diagonals bisect each other. So the midpoint of the given opposite vertices is also the midpoint of the other diagonal.
Midpoint = $\left(\dfrac{2 + (-3)}{2}, \dfrac{1 + (-4)}{2}\right) = \left(-\dfrac{1}{2}, -\dfrac{3}{2}\right)$
Since the other two vertices lie on $x + 9y +

The points (2,1)(2,1)(2,1) and (−3,−4)(-3,-4)(−3,−4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x+9y+c=0x + 9y + c = 0x+9y+c=0, then ccc is

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