Question

Identify the transformation that carries the figure onto itself.

A) reflect across the line x = 6 and rotate 900° clockwise about (6, 7)
B) reflect across the line y = 7 and rotate 990° clockwise about (6, 7)
C) reflect across the line x = 7 and rotate 900° clockwise about (6, 7)
D) reflect across the line y = 6 and rotate 990° clockwise about (6, 7)

Answer 1

Answer:option b is correct

Explanation:

Answer 2

The correct option is A.

Explanation:

The coordinates of rectangle are (5,5), (7,5),(7,9) and (5,9).

If the reflected across the line x=6, it will give the same rectangle because x=6 is line of symmetry.

`900=(720+180)=2(360)+180`

It means 900 degree clockwise means 180 degree clockwise about (6,7).

Since (6,7) is a center of rectangle. If a rectangle rotated at 180 degree clockwise about center, then it will give the same rectangle.

If a figure rotates 180 degree clockwise about origin, then

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

If a figure rotates 180 degree clockwise about (a,b), then

`(x,y)\rightarrow (2a-x,2b-y)`

The coordinates after reflection are (5,5), (7,5),(7,9) and (5,9).

The coordinates after rotation are

`(5,5)\rightarrow (2(6)-5,2(7)-5)\rightarrow (7,9)`

`(7,5)\rightarrow (2(6)-7,2(7)-5)\rightarrow (5,9)`

`(7,9)\rightarrow (2(6)-7,2(7)-9)\rightarrow (5,5)`

`(5,9)\rightarrow (2(6)-5,2(7)-9)\rightarrow (7,5)`

The coordinates after reflection followed by rotation are (5,5), (7,5),(7,9) and (5,9).

After the transformation the figure onto itself. Therefore option A is correct.