Question What is the image point of \( (2,-4) \) after the transformation \( r_{y=x} \circ T_{0,0} \) ?
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To find the image point of \( (2,-4) \) after the transformation \( r_{y=x} \circ T_{0,0} \), we first note that \( T_{0,0} \) is the translation by the vector \( (0,0) \), which does not change the point. So the point remains \( (2, -4) \). Next, we apply the reflection transformation \( r_{y=x} \), which reflects a point over the line \( y = x \). This transformation swaps the coordinates of the point. Therefore, the image point of \( (2, -4) \) will become \( (-4, 2) \). The final answer is \( (-4, 2) \).
