Question

Graph the reflection of rectangle PQRS under a reflection across the given line.

Answer 1

The line graphed is the line:

$y=x$

A reflection over this line is a special case where each pre-image point (x,y) is transformed as follows:

$(x,y)=(y,x)$

So, first, le's identify each vertex:

$\begin{gathered} P\colon(-2,5) \\ Q\colon(1,2) \\ R\colon(-3,-2) \\ S\colon(-6,1) \end{gathered}$

Now, we apply the transformation on each.

$\begin{gathered} (x,y)\to(y,x) \\ P\colon(-2,5)\to(5,-2) \\ Q\colon(1,2)\to(2,1) \\ R\colon(-3,-2)\to(-2,-3) \\ S\colon(-6,1)\to(1,-6) \end{gathered}$

Now, we plot these image points: