Which of the steps will cause the rectangle to map onto itself?
a. reflect across the y-axis, then shift 6 units right
b. reflect across the y-axis, then shift 7 units right
c. reflect across the y-axis, then shift 9 units right
d. reflect across the y-axis, then shift 8 units right

Reflect across the y-axis, then shift 9 units right

C is correct.

Step-by-step explanation:

We are given a rectangle on coordinate plane. ABCD is a rectangle.

First we write the coordinate of ABCD

A(1,3)   B(1,6)    C(8,6)     D(8,3)

Now we reflect across y-axis and write new coordinate of ABCD

Reflection across y-axis: (x,y) -> (-x,y)

A(1,3)   →  A'(-1,3)

B(1,6)   →  B'(-1,6)

C(8,6)  →  C'(-8,6)

D(8,3)  →  D'(-8,3)

We need to find same rectangle. If we overlap the coordinate with original one we will get similar rectangle same position and shape.

If we shift A'(-1,3) to D(8,3)  we will set original rectangle.

Now we will see which operation will get A' to D

If we shift point A' 9 unit right then get point D

A'(-1,3)  shift 9 unit right A'(-1+9,3) => A'(8,3) = D(8,3)

Hence, Reflect across the y-axis, then shift 9 units right