8. find the glide reflection image of the black triangle where the translation is (x,y) -> (x,y - 7) and the line of reflection is x = 1. am i correct?

Option D is correct.

Explanation:

From the given figure,

Labelled the black triangle as A, B and C

The coordinates of  triangle ABC are;

A= (2,8) , B= (2,5) and C=(6,5)

To find the glide reflection image of the triangle ABC.

Glide Reflection: It is a composition of transformations.

In glide reflection, a translation is first performed on the figure then it is reflected over a line.

Given: The rule of translation is: and line of reflection is x= 1.

Now, apply the rule of translation on black triangle, we get;

= A' (2,1)

=B' (2,-2)

= C' (6,-2)  

Next,

Apply the rule of reflection over the line x =1,

i.e,

=A" (0,1)

=B" (0,-2) and

=C" (-4,-2)

You can see the graph of Glide reflection as shown below in the attachment.