Question

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

Answer 1

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

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

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.

Answer 2

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.