9.5 & 9.6 – Compositions of Transformations & Symmetry

Glide Reflection: A transformation with a translation and then a reflection in a line parallel to the direction of the translation k Q P

Composition of Transformations: Any two transformations combined to form a single transformation

If lines k and m are parallel, then a reflection in line k followed by a reflection in line m is a ___________. If ____ is the image of P after the two reflections, then: translation

If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is a _________. If ____ is the image of P after the two reflections, then: rotation The angle of rotation is 2x°, where x° is the measure of the acute or right angle formed by k and m

A 1. Translation: (x, y) → (x + 2, y) Reflection: in the x-axis Graph the image of A(1, –2) after the described glide reflection. 1. Translation: (x, y) → (x + 2, y) Reflection: in the x-axis A

A 2. Translation: (x, y) → (x – 1, y + 3) Reflection: in x = 2 Graph the image of A(1, –2) after the described glide reflection. 2. Translation: (x, y) → (x – 1, y + 3) Reflection: in x = 2 A

The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3) The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3). Graph the image of ABC after a composition of the transformations in the order they are listed. Reflection: y-axis Translation: (x, y) → (x + 3, y – 5) B C A

(x, y) → (y, x) B (3, 1) (1, 3) C (1, –3) A (–3, 1) (5, –1) (–1, 5) The vertices of ABC are A(3, 1), B(1, 5) and C(5, 3). Graph the image of ABC after a composition of the transformations in the order they are listed. Reflection: y = 1 Reflection: y = x (x, y) → (y, x) B (3, 1) (1, 3) C (1, –3) A (–3, 1) (5, –1) (–1, 5)

Describe the composition of transformations. Reflection: x-axis Translation: (x, y) → (x + 6, y + 2)

Describe the composition of transformations. Rotation: 90° Reflection: x-axis

In the diagram, is reflected in line r, and is reflected in line s. 7. A translation maps onto which segment?

In the diagram, is reflected in line r, and is reflected in line s. 8. Which lines are perpendicular to r and s

In the diagram, is reflected in line r, and is reflected in line s. 9. Name a segment parallel to

In the diagram, is reflected in line r, and is reflected in line s. 10. If the distance between r and s is 2.4 inches, what is the length of 2.4  2 4.8 inches

In the diagram, is reflected in line r, and is reflected in line s. 11. Is the distance from to r the same as the distance from C to r? Yes, Def. of Reflection

12. Find the angle of rotation that maps T onto 75  2 150°

13. Find the angle of rotation that maps A onto 99  2 198°

Line of Symmetry: The figure can be mapped onto itself by a reflection in the line Rotational Symmetry: The figure can be mapped onto itself by a rotation of 180° or less around a point

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 1 Line: _____________ Rotational: _________ none

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. none Line: _____________ Rotational: _________ none

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 360 3 = 120° 3 Line: _____________ Rotational: _________ 120°

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 360 4 = 90° 4 Line: _____________ Rotational: _________ 90°, 180°

Rotational: ____________ Identify the number of line and rotational symmetry of the figure shown. 360 6 = 60° 6 Line: _____________ Rotational: ____________ 60°, 120°, 180°

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 1 Line: _____________ Rotational: _________ none

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 360 4 = 90° 4 Line: _____________ Rotational: _________ 90°, 180°

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 1 Line: _____________ Rotational: _________ none

Rotational: _________ Identify the number of line and rotational symmetry of the figure shown. 360 2 = 180° Line: _____________ Rotational: _________ 2 180°

HW Problems 9.5 #13 Translation: Rotation: 180° 9.6 611-612 621-623 3, 6, 9, 11, 13-21 all 3, 4, 6, 7, 9, 11, 12 9.5 #13 Translation: (x, y) → (x + 5, y + 1) Rotation: 180°