Answer:
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: [tex](x,y) \rightarrow (x, y-7)[/tex] and line of reflection is x= 1.
Now, apply the rule of translation on black triangle, we get;
[tex]A (2,8) \rightarrow (2, 8-7)[/tex] = A' (2,1)
[tex]B (2,5) \rightarrow (2, 5-7)[/tex] =B' (2,-2)
[tex]C (6,5) \rightarrow (6, 5-7)[/tex] = C' (6,-2)
Next,
Apply the rule of reflection over the line x =1,
i.e, [tex](x,y) \rightarrow (-x+2, y)[/tex]
[tex]A' (2,1) \rightarrow (-2+2, 1)[/tex] =A" (0,1)
[tex]B' (2,-2) \rightarrow (-2+2, -2)[/tex] =B" (0,-2) and
[tex]C' (6,-2) \rightarrow (-6+2, -2)[/tex] =C" (-4,-2)
You can see the graph of Glide reflection as shown below in the attachment.
