Question

Identify the transformation that carries the figure onto itself.

A) reflect across the line y = 7 and rotate 270° clockwise about (−7, 8)
B) reflect across the line x = 7 and rotate 270° clockwise about (−7, 8)
C) reflect across the line y = −7 and rotate 540° clockwise about (−7, 8)
D) reflect across the line x = −7 and rotate 540° clockwise about (−7, 8)

Answer 1

D. Reflect across line x =-7

Answer 2

The correct option is D.

Explanation:

The vertices of given figure are (-9,8), (-7,7), (-5,8), (-7,9).

1. If figure reflect across the line y = 7, then

`(x,y)\rightarrow (x,14-y)`

The vertices of image are (-9,6), (-7,7), (-5,6), (-7,5).

Then rotate 270° clockwise about (−7, 8).

`(x,y)\rightarrow (-y+1,x+15)`

The vertices of image are (-5,6), (-6,8), (-5,10), (-4,8). These are not the vertices of given figure, theretofore option A is incorrect.

2. If figure reflect across the line x = 7, then

`(x,y)\rightarrow (-x+14,y)`

The vertices of image are (23,8), (21,7), (19,8), (21,9).

Then rotate 270° clockwise about (−7, 8).

`(x,y)\rightarrow (-y+1,x+15)`

The vertices of image are (-7,38), (-6,36), (-7,34), (-8,36). These are not the vertices of given figure, theretofore option B is incorrect.

3. If figure reflect across the line y = -7, then

`(x,y)\rightarrow (x,-y-14)`

The vertices of image are (-9,-22), (-7,-21), (-5,-22), (-7,-23).

Then rotate 540° clockwise about (−7, 8).

`(x,y)\rightarrow (-x-14,-y+16)`

The vertices of image are (-5,38), (-7,37), (-9, 38), (-7.39). These are not the vertices of given figure, theretofore option C is incorrect.

4. If figure reflect across the line x = -7, then

`(x,y)\rightarrow (-x-14,y)`

The vertices of image are (-5,8), (-7,7), (-9,8), (-7,9).

Then rotate 540° clockwise about (−7, 8).

`(x,y)\rightarrow (-x-14,-y+16)`

The vertices of image are (-9,8), (-7,9), (-5,8), (-7,7). These are the vertices of given figure, theretofore option D is correct.