Question

what is the image point of $(-8,2)$ after the transformation $r_{y = x}circ t_{-3,3}$?

Explanation:

Step1: Translation

The translation \(T_{-3,3}\) means we subtract \(3\) from the \(x\) - coordinate and add \(3\) to the \(y\) - coordinate.
For the point \((-8,2)\), after translation:
\(x=-8 - 3=-11\), \(y = 2+3=5\). The point becomes \((-11,5)\).

Step2: Reflection over the line \(y = x\)

The rule for reflection over the line \(y=x\) is \((x,y)\to(y,x)\).
For the point \((-11,5)\), after reflection: \(x = 5\), \(y=-11\).

Answer:

\((5,-11)\)