Answer:
Step-by-step explanation:
a) You are told the transformation is ...
... (x, y) ⇒ (x -5, y +2)
Point A is (x, y) = (2, -2). Putting these values in the transformation formula gives ...
... (2, -2) ⇒ (2-5, -2+2) = (-3, 0)
The coordinates of A' after the translation are (-3, 0).
___
b) Reflection across the line y=x simply interchanges the x and y coordinates. The formula is ...
... (x, y) ⇒ (y, x)
Your point S is (-2, -5). Putting these values in the transformation formula gives ...
... (-2, -5) ⇒ (-5, -2)
The coordinates of S' after the transformation are (-5, -2).
_____
Comment on attachments
I added the image showing the coordinates of ABC, just so the whole problem statement is in one place. The second attachment shows the reflection of S across the line y = x.
