SOLUTION

EXAMPLE 1Find the image of a glide reflection

The vertices of ABC are A(3, 2), B(6, 3), and C(7, 1). Find the image of ABC after the glide reflection.

Translation: (x, y) →Reflection: in the x-axis

(x –12, y)

Begin by graphing ABC. Then graph A′B′C′ after a translation 12 units left. Finally, graph A′′B′′C′′ after a reflection in the x-axis.

GUIDED PRACTICE for Example 1

1. Suppose ABC in Example 1 is translated 4 units down, then reflected in the y-axis. What are the coordinates of the vertices of the image?

SOLUTION

A(3, 2) → A′(3, – 2)

B(6, 3) → B′(6, – 1)

C(7, 1) → C′(7, – 3)

(x, y) (x , y – 4 )

(x, y) → (–a, b)Reflection: in the y-axis

→ A"(–3, – 2)

→ B"(–6, – 1)

→ C"(–7, – 3)

Translation: (x, y) (x , y – 4 )

→ (–a, b)

GUIDED PRACTICE for Example 1

2. In Example 1, describe a glide reflection from A′′B′′C′′ to ABC.

SOLUTION

Reflection: in the x-axisTranslation: (x, y) → (x +12, y)

Begin by graphing A′B′C′. Then graph ABC after a translation 12 units right. Finally, graph ABC after a reflection in the x-axis.