Answer: (12,3)
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Explanation:
R is located at (3,4). Move it 3 units to the left and 4 units down to have it move to (0,0). Call this point A. Apply the same translation rule to point B so that (2,-5) moves to (-1,-9). Let's call this point C
Now you'll use the rule [tex](x,y) \to (-y,x)[/tex] which rotates any point around the origin 90 degrees counterclockwise. So we're rotating C around A.
Point C has the coordinates (-1,-9). When you use the rotation rule [tex](x,y) \to (-y,x)[/tex] we get [tex](-1,-9) \to (-(-9), -1) = (9, -1)[/tex]. We'll call this point D
Finally, undo the translation rule done at the start of the problem. So we'll go 3 units to the right and 4 units up to have point D move to point E = (12,3) which is exactly where point B' is located.
Check out the diagram below.
