Question

A figure lies on a coordinate plane with point B located at (2,-5). The figure is rotated 90 degrees counter-clockwise around a point R located at (3,4). What will be the coordinates of B'?

Answer 1

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 $(x,y) \to (-y,x)$ 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 $(x,y) \to (-y,x)$ we get $(-1,-9) \to (-(-9), -1) = (9, -1)$. 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.