Question

1. what is the image point of (-6, 7) after the transformation $r_{y=-x} \circ t_{-3, -5}$?

Explanation:

Step1: Translation

The translation \(T_{-3,-5}\) means \((x,y)\to(x - 3,y-5)\).
For the point \((-6,7)\), after translation:
\(x=-6-3=-9\), \(y = 7-5 = 2\). The point becomes \((-9,2)\).

Step2: Reflection

The reflection \(r_{y=-x}\) has the rule \((x,y)\to(-y,-x)\).
For the point \((-9,2)\), after reflection:
\(x=-2\), \(y = 9\).

Answer:

\((-2,9)\)