$PQRS$ is a convex quadrilateral.Find the area of $PQRS.$

Question

Let $P$ be the point $(3,2).$Let $Q$ be the reflection of $P$ about the $x-axis.$Let $R$ be the reflection of $Q$ about the line $y=-x$ and let $S$ be the reflection of $R$ through the origin.$PQRS$ is a convex quadrilateral.Find the area of $PQRS.$

I found out coordinates of $Q$ as $(3,-2)$ but then i could not find the coordinates of $R$ and $S$ and then i am stuck.Please help me.

Answer 1

Hint: Reflecting the point $(x|y)$ about the line $y=-x$ yields the point $(-y|-x)$..(Why?). Reflecting the point $(x|y)$ through the origin yields the point $(-x|-y)$..(Why?)

You should now be able to compute the coordinates of the remaining points and finally the area of $PQRS$.