Answer:
The correct option is c.
Step-by-step 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
[tex](x,y)\rightarrow (x+2,y+8)[/tex]
The vertices of pentagon after translation.
[tex]A(-5,-2)\rightarrow A_1(-3,6)[/tex]
[tex]B(-7,-3)\rightarrow B_1(-5,5)[/tex]
[tex]C(-6,-6)\rightarrow C_1(-4,2)[/tex]
[tex]D(-3,-5)\rightarrow D_1(-1,3)[/tex]
[tex]E(-3,-3)\rightarrow E_1(-1,5)[/tex]
If the figure reflected across y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
The vertices of pentagon after translation by rule [tex](x,y)\rightarrow (x+2,y+8)[/tex] followed by reflection across y-axis are
[tex]A_1(-3,6)\rightarrow A'(3,6)[/tex]
[tex]B_1(-5,5)\rightarrow B'(5,5)[/tex]
[tex]C_1(-4,2)\rightarrow C'(4,2)[/tex]
[tex]D_1(-1,3)\rightarrow D'(1,3)[/tex]
[tex]E_1(-1,5)\rightarrow E'(1,5)[/tex]
The pentagon ABCDE translated according to the rule [tex](x,y)\rightarrow (x+2,y+8)[/tex] and reflected across the y-axis to create A'B'C'D'E'.
Therefore, the correct option is c.
