A parallelogram has three consecutive vertices $(-3,4)$, $(0,-4)$ and $(5,2)$. The fourth vertex is

• Correct answer
  A

  $(2,10)$
• B

  $(2,9)$
• C

  $(3,9)$
• D

  $(4,10)$

Solution

Let $A B C D$ is a parallelogram as shown in figure. Point $O$ is the point of intersection of two diagonals.
Point ' $O$ ' $=\left(\frac{-3+5}{2}, \frac{4+2}{2}\right)=(1,3)$. Now, point ' $O$ ' bisect diagonal $B D$. $\begin{aligned} & 1=\frac{x+0}{2} \Rightarrow x=2 \\ & 3=\frac{y-4}{2} \Rightarrow y=10 .\end{aligned}$ $\therefore$ Fourth vertices $D(x, y)=(2,10)$.

Hence, the correct answer is option: 'A'.