Question

question
what is the image point of (2, -4) after the transformation $r_{y=x} \circ t_{0,0}$?
answer attempt 1 out of 2

Explanation:

Step1: Analyze the transformation \( T_{0,0} \)

The transformation \( T_{0,0} \) is the identity translation (no translation, since we are translating by \( (0,0) \)). So the point \( (2, - 4) \) remains \( (2,-4) \) after \( T_{0,0} \).

Step2: Apply the reflection \( r_{y = x} \)

The reflection over the line \( y=x \) swaps the \( x \)-coordinate and the \( y \)-coordinate of a point \( (a,b) \). So for the point \( (2,-4) \), after reflection over \( y = x \), the new point is \( (-4,2) \).

Answer:

\((-4, 2)\)