Rectangle STUV is shown on a coordinate plane. If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, what is the location of S″?

Question

If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, what is the location of S″?

 (3, −9) 

(3, −4)

 (−2, −4) 

(−2, −9)

Answer 1

It's nearly impossible to add a useful figure with more than a few lines without exceeding the Wyzant size (KB) limit. Here's a figure to accompany the answer given by Martin C.

Answer 2

The answer is (-2, -9). To see why, first note that the translation "down 4 and left 2" described in the problem moves S, whose coordinates are (-7, 6), to (-9, 2). Then, rotating the plane 90° counterclockwise about the origin moves a generic point (x, y) to (-y, x). I would like to show why this is the case, but cannot draw on this answer screen. It helps to think in terms of the quadrants of the plane; rotating 90° counterclockwise moves a point in quadrant I into quadrant II, where x is negative and y positive. Applying (x, y) → (-y, x) to (-9, 2) results in (-2, -9).