Question

Which rectangle if translated 6 units down and then rotated 90° clockwise about the point (-5, -5) will result in rectangle E?

A) Rectangle A

B) Rectangle B

C) Rectangle C

D) Rectangle D

Answer 1

B) Rectangle B

Explanation:

When vertex (-5,1) is moved 6 units down, it goes to (-5, 1-6) = (-5,5)

This points remains unchanged after rotation because it is the point about which the rotation is taking place

Answer 2

B

Explanation:

Basically, in order to figure out the original rectangle, we need to "undo" the transformations by performing them backwards. In other words, we need to first do a rotation before the translation.

Since originally, the rectangle was rotated 90 degrees clockwise, to undo this, we need to rotate Rectangle E 90 degrees counterclockwise about (-5, -5). When we do so, we see that our coordinates become (-5, -5), (-7, -5), (-7, -2), and (-5, -2).

Now, since previously the rectangle was moved down 6 units, we need to translate Rectangle E 6 units up. When we translate vertically, only the y-coordinates change. Here, since we're moving up 6 units, each y-coordinate will increase by 6. So, we go from (-5, -5), (-7, -5), (-7, -2), and (-5, -2) to:

(-5, -5 + 6) = (-5, 1)

(-7, -5 + 6) = (-7, 1)

(-7, -2 + 6) = (-7, 4)

(-5, -2 + 6) = (-5, 4)

Matching these coordinates is Rectangle B, so that's the answer.

Hope this helps!