Question

If $(-6,-4)$ and $(3,5)$ are the extremities of the diagonal of a parallelogram and $(-2,1)$ is its third vertex, then its fourth vertex is

• A. $(-5,2)$
• B. $(0,-1)$
• C. $(-1,1)$
• D. none of these

Answer 1

The correct option is A $(-5,2)$

Let $P(-6,-4),Q(2,-1),R(3,5),S(x,y)$
The two diagonals of a parallelogram bisect each other.
$\therefore$ Midpoint of PR$=$Midpoint of QS.
$PR=(\frac{-6+3}{2},\frac{-4+5}{2})=(\frac{-3}{2},\frac{1}{2})QS=(\frac{2+x}{2},\frac{-1+y}{2})ATPPR=QS\frac{2+x}{2}=\frac{-3}{2}\frac{-1+y}{2}=\frac{1}{2}x=-5y=2S(-5,2)$
Hence option (A) is correct.