Question

Which two transformations are applied to pentagon ABCDE to create A’B’C’D’E’?

Answer 1

The pentagon was reflected across the x-axis. By looking at Point A, you can see x was increased 8, x+8. Also, y was increased by 2, y+2.

Answer 2

The correct option is c.

Explanation:

From the given figure it is clear that the vertices of preimage are A(-5,-2), B(-7,-3), C(-6,-6), D(-3,-5) and E(-3,-3).

The vertices of image are A'(3,6), B'(5,5), C'(4,2), D'(1,3) and E'(1,5).

If figure translated 2 units right and 8 units up then

`(x,y)\rightarrow (x+2,y+8)`

The vertices of pentagon after translation.

`A(-5,-2)\rightarrow A_1(-3,6)`

`B(-7,-3)\rightarrow B_1(-5,5)`

`C(-6,-6)\rightarrow C_1(-4,2)`

`D(-3,-5)\rightarrow D_1(-1,3)`

`E(-3,-3)\rightarrow E_1(-1,5)`

If the figure reflected across y-axis, then

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

The vertices of pentagon after translation by rule
`(x,y)\rightarrow (x+2,y+8)` followed by reflection across y-axis are

`A_1(-3,6)\rightarrow A'(3,6)`

`B_1(-5,5)\rightarrow B'(5,5)`

`C_1(-4,2)\rightarrow C'(4,2)`

`D_1(-1,3)\rightarrow D'(1,3)`

`E_1(-1,5)\rightarrow E'(1,5)`

The pentagon ABCDE translated according to the rule
`(x,y)\rightarrow (x+2,y+8)` and reflected across the y-axis to create A'B'C'D'E'.

Therefore, the correct option is c.