Find the glide reflection image of the blue triangle where the translation is (x , y) → (x , y - 7) and the line of reflection is x = 1.

Solution:

From the given figure,

Label the blue 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 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 (x , y) to (x , y - 7)

Line of reflection is x = 1.

Applying the rule of translation on blue triangle,

A(2 , 8) → (2 , 8 - 7) = A’(2 , 1)

B(2 , 5) → (2 , 5 - 7) = B’(2 , -2)

C(6 , 5) → (6 , 5 - 7) = C’(6 , -2)

Next, apply the rule of reflection over the line x=1,

I.e,(x , y) → (-x + 2 , y)

A’(2 , 1) → (-2 + 2 , 1) = A’’(0 , 1)

B’(2 , -2) → (-2 + 2 , -2) = B’’(0 , -2)

C’(6 , -2) → (-6 + 2 , -2) = C’’(-4 , -2)

Therefore, A’’(0 , 1) B’’(0 , -2) and C’’(-4 , -2)

Find the glide reflection image of the blue triangle where the translation is (x , y) → (x , y - 7) and the line of reflection is x = 1.

Summary:

The glide reflection image of the blue triangle where the translation is (x , y) → (x , y - 7) and the line of reflection is x = 1 are A’(2 , 1) B’(2 , -2) C’(6 , -2) and A’’(0 , 1) B’’(0 , -2) and C’’(-4 , -2).