CAT 2020 Slot 3 QA Question & Solution
GeometryMedium
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
Options
12
13
15
14
Solution
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) = ($\frac{2-3}{2},\frac{1-4}{2}$) = (-1/2 , -3/2)
Keeping this cordinates in the above line equation, we get c = 14