Question

Which rectangle if reflected over the x-axis and then translated 8 units right will result in rectangle E?

A) Rectangle A

B) Rectangle B

C) Rectangle C

D) Rectangle D

Answer 1

Answer: Rectangle D

Explanation:

Answer 2

Rectangle D is reflected over the x-axis and then translated 8 units right will result in rectangle E

Explanation:

The coordinates of rectangle D are:

(-1, 1)

(-1, 4)

(-3, 1) and

(-3, 4)

The rule of reflection across x-axis is given by:

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

`(-1, 1) \rightarrow (-1 , -1)`

`(-1, 4) \rightarrow (-1 , -4)`

`(-3, 1) \rightarrow (-3 , -1)`

`(-3, 4) \rightarrow (-3 , -4)`

Next, translate this 8 unit right which is given by:

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

`(-1, -1) \rightarrow (-1+8 , -1) =(7, -1)`

`(-1, -4) \rightarrow (-1+8 , -4) =(7, -4)`

`(-3, -1) \rightarrow (-3+8 , -1) =(5, -1)`

`(-3, -4) \rightarrow (-3+8 , -4) =(5, -4)`

⇒(7, -1) , (5, -1) , (5, -4) and (7, -4) represents the coordinate of rectangle E.

Therefore, Rectangle D if reflected over the x-axis and then translated 8 units right will result in rectangle E