Question

A glide reflection is a transformation that is made up of a translation and a reflection across a line the is parallel to the direction of the translation.

Part A. Graph triangle DEF with vertices D(1,-1) E(7,-3) F(2,-7)
Part B. Graph triangle DEF under a glide reflection where the translation is (x,y) —> (x, y+8). Give the coordinates of the vertices of the image.
Part C. Are the two figures congruent?

Answer 1

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.