Question

Three vertices of rhombus taken in order are $(2,-1),(3,4)$ and $(-2,3)$. Find the fourth vertex.

• A. $(1,2)$
• B. $(-3,-2)$
• C. $(3,2)$
• D. None of these

Answer 1

The correct option is B $(-3,-2)$

Let M be the mid point of one diagonal formed by (2, -1) and (-2, 3) then using mid-point method;

Coordinate of $M(\frac{2+(-2)}{2},\frac{-1+3}{2})=(0,1)$
$\Rightarrow (\frac{x+3}{2},\frac{y+4}{2})=(0,1)$
$\Rightarrow x=-3$ and $y=-2$
$\therefore (-3,-2)$ is coordinate of $D$