Answer:
(-2, 1)
Step-by-step explanation:
Rotation 90° effects the transformation ...
(x, y) ⇒ (-y, x)
Translation by (-4, -1) effects the transformation ...
(x, y) ⇒ (x -4, y -1)
So, the translation of the rotated figure results in the overall transformation ...
(x, y) ⇒ (-y -4, x -1)
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We have the transformed figure, so need to find the inverse transformation. Solving x = -y-4, we find y = -(x+4). Solving y = x-1, we find x = y+1. So to "undo" the translated rotated figure, we need to apply the transform ...
(x, y) ⇒ (y +1, -(x +4))
For A''(-5, -3), we have ...
A = (-3+1, -(-5+4)) = (-2, 1) . . . . . matches the 4th choice
