Question

Given rectangles ABCD and A'B'C'D, describe the transformation that takes place from ABCD to A'B'C'D'

Answer 1

A 90° clockwise rotation about the origin and a translation of 7 units down.

Answer 2

A 90° clockwise rotation about the origin and a translation of 7 units down.

Explanation:

First of all, we need to define the image and pre-image.

• The pre-image is the rectangle ABCD, before the transformation.
• The image is the rectangle A'B'C'D', after the transformation.

Second, let's write down the coordinates of each rectangle.

ABCD coordinates:

A(-6,5)

B(-1,5)

C(-1,1)

D(-6,1)

A'B'C'D' coordinates:

A'(5,-1)

B'(5,-6)

C'(1,-6)

D'(1,-1)

The first rule we need to apply is the 90° clockwise rotation which is

`(x,y) \implies (y,-x)`

Which gives us (5,6), (5,1), (1,1), (1,6).

Then, we use the 7 units-down rule

`(x,y) \implies (x,y-7)`

Which gives us (5,-1), (5,-6), (1,-6) and (1,-1).

Therefore, the right answer is the third choice.