Question

The coordinates of points $P(-2,2),Q(3,2)$ and $R(3,-2)$ are the vertices of a rectangle $PQRS$`. What are the coordinates of S?

• A. $(-3,-2)$
• B. $(-2,-2)$
• C. $(3,2)$
• D. $(2,2)$

Answer 1

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

Mid-point of $PR=(\frac{-2+3}{2},\frac{2-2}{2})=(\frac{1}{2},0)$

Let coordinate of $S=(x,y)$

Mid-point of $QS=(\frac{3+x}{2},\frac{2+y}{2})$

Mid-point of $PR=$Mid-point of $QS$

$\Rightarrow (\frac{1}{2},0)=$$(\frac{3+x}{2},\frac{2+y}{2})$

We have $\frac{1}{2}=\frac{3+x}{2}$

$\Rightarrow x=-2$ and $0=\frac{2+y}{2}$

$\Rightarrow y=-2$

Coordinate of $S=(-2,-2)$

Hence, B is the correct option.