composition of transformations glide reflection Vocabulary

Concept

Graph a Glide Reflection Quadrilateral BGTS has vertices B(–3, 4), G(–1, 3), T(–1 , 1), and S(–4, 2). Graph BGTS and its image after a translation along 5, 0 and a reflection in the x-axis. Example 1

Step 1 translation along 5, 0 (x, y) → (x + 5, y) Graph a Glide Reflection Step 1 translation along 5, 0 (x, y) → (x + 5, y) B(–3, 4) → B'(2, 4) G(–1, 3) → G'(4, 3) S(–4, 2) → S'(1, 2) T(–1, 1) → T'(4, 1) Example 1

Step 2 reflection in the x-axis (x, y) → (x, –y) B'(2, 4) → B''(2, –4) Graph a Glide Reflection Step 2 reflection in the x-axis (x, y) → (x, –y) B'(2, 4) → B''(2, –4) G'(4, 3) → G''(4, –3) S'(1, 2) → S''(1, –2) T'(4, 1) → T''(4, –1) Answer: Example 1

Concept

Graph Other Compositions of Isometries ΔTUV has vertices T(2, –1), U(5, –2), and V(3, –4). Graph ΔTUV and its image after a translation along –1 , 5 and a rotation 180° about the origin. Example 2

Step 1 translation along –1 , 5 (x, y) → (x + (–1), y + 5) Graph Other Compositions of Isometries Step 1 translation along –1 , 5 (x, y) → (x + (–1), y + 5) T(2, –1) → T'(1, 4) U(5, –2) → U'(4, 3) V(3, –4) → V'(2, 1) Example 2

Step 2 rotation 180 about the origin (x, y) → (–x, –y) Graph Other Compositions of Isometries Step 2 rotation 180 about the origin (x, y) → (–x, –y) T'(1, 4) → T''(–1, –4) U'(4, 3) → U''(–4, –3) V'(2, 1) → V''(–2, –1) Answer: Example 2

GSP Demo…

Concept

Concept

Reflect a Figure in Two Lines Copy and reflect figure EFGH in line p and then line q. Then describe a single transformation that maps EFGH onto E''F''G''H''. Example 3

Step 1 Reflect EFGH in line p. Reflect a Figure in Two Lines Step 1 Reflect EFGH in line p. Example 3

Step 2 Reflect E'F'G'H' in line q. Reflect a Figure in Two Lines Step 2 Reflect E'F'G'H' in line q. Answer: EFGH is transformed onto E''F''G''H'' by a translation down a distance that is twice the distance between lines p and q. Example 3

Concept