cat 2020 Question 25

Question

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

Accepted Answer

The midpoints of two diagonals of a parallelogram are the same

Hence the midpoint of (2,1) and (-3,-4) lie on x + 9y + c = 0

midpoint of (2,1) and (-3,-4) = $\left( \frac{2-3}{2}, \frac{1-4}{2} \right) = \left( -\frac12, -\frac32 \right) $

Keeping this point in the above line equation, we get c = 14

Question 25.