Answer:
Rectangle D is reflected over the x-axis and then translated 8 units right will result in rectangle E
Step-by-step 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:
[tex](x, y) \rightarrow (x , -y)[/tex]
[tex](-1, 1) \rightarrow (-1 , -1)[/tex]
[tex](-1, 4) \rightarrow (-1 , -4)[/tex]
[tex](-3, 1) \rightarrow (-3 , -1)[/tex]
[tex](-3, 4) \rightarrow (-3 , -4)[/tex]
Next, translate this 8 unit right which is given by:
[tex](x, y) \rightarrow (x+8 , y)[/tex]
[tex](-1, -1) \rightarrow (-1+8 , -1) =(7, -1)[/tex]
[tex](-1, -4) \rightarrow (-1+8 , -4) =(7, -4)[/tex]
[tex](-3, -1) \rightarrow (-3+8 , -1) =(5, -1)[/tex]
[tex](-3, -4) \rightarrow (-3+8 , -4) =(5, -4)[/tex]
⇒(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
