CAT 2020 Quant Question [Slot 3] with Solution 18

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

1. 12
2. 14
3. 13
4. 15
Option: 2
Solution:

The given line also passes through the point of intersection of the diagonals of the parallelogram, which is the mid-point of (2,1) and (-3,-4) The mid-point of the given two points is (-1/2, -3/2).

Substituting the point in the given equation $- \frac{1}{2} + 9 \times \frac{{ - 3}}{2} + c = 0 \Rightarrow c = 14$

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