SOLUTION EXAMPLE 1 Find 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.

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SOLUTION EXAMPLE 1 Find 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 -axis Translation : (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.