12-5 Graphing Rotations Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up Parallelogram ABCD has vertices (-4, 1), (0, 1), (–3, 4), and (1, 4). 1. What are the vertices of ABCD after it has been reflected across the x-axis? 2. What are the vertices after is has been reflected across the y-axis? (–4, –1), (0, –1), (–3, –4), (1, –4) (4, 1), (0, 1), (3, 4), (–1, 4) Course Graphing Rotations

Problem of the Day If each of the capital letters of the alphabet is rotated a half turn around its center, which will look the same? H, I, N, O, S, X, Z Course Graphing Rotations

Learn to use rotations to change positions of figures on a coordinate plane. Course Graphing Rotations

You can rotate a figure about the origin or another point on a coordinate plane. Course Graphing Rotations

A rotation is the movement of a figure about a point. Rotating a figure “about the origin” means that the origin is the center of rotation. Remember! Course Graphing Rotations

y x Additional Example 1: Rotating Figures on a Coordinate Plane EF GH Course Graphing Rotations Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH clockwise 90° about the origin.

Additional Example 1 Continued The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. EFGHE’F’G’H’ E(–4, 0)E’(0, 4) F(0, 0)F’(0, 0) G(–2, –3)G’(–3, 2) H(–6, –3)H’(–3, 6) Course Graphing Rotations

Additional Example 1 Continued Rotate parallelogram EFGH 90° about the origin y x E F GH F’F’ E’E’ G’G’ H’H’ Course Graphing Rotations

y x Try This: Example 1 Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH counterclockwise 180° about the origin. EF GH Course Graphing Rotations

Try This: Example 1 Continued The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. EFGHE’F’G’H’ E(–4, 0)E’(4, 0) F(0, 0)F’(0, 0) G(–2, –3)G’(2, 3) H(–6, –3)H’(6, 3) Course Graphing Rotations

y x Try This: Example 1 Continued Rotate parallelogram EFGH counterclockwise 180° about the origin. EF GH E’F’F’ G’G’ H’H’ Course Graphing Rotations

Additional Example 2A: Art Application An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin y x C D B A E Course Graphing Rotations

ABCDEA’B’C’D’E’ A(0, 0)A’(0, 0) B(1, 4)B’(4, –1) C(3, 5)C’(5, –3) D(7, 3)D’(3, –7) Additional Example 2A Continued E(6, 0)E’(0, –6) The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. Course Graphing Rotations

Additional Example 2A Continued Rotate the figure after a clockwise 90° about the origin y x C D B A E C’C’ D’D’ B’B’ A’A’ E’E’ Course Graphing Rotations

B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin. Additional Example 2B: Art Application y x C D B A E Course Graphing Rotations

The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Additional Example 2B Continued ABCDEA’B’C’D’E’ A(0, 0)A’(0, 0) B(1, 4)B’(–1, –4) C(3, 5)C’(–3, –5) D(7, 3)D’(–7, –3) E(6, 0)E’(–6, 0) Course Graphing Rotations

Additional Example 2B Continued Rotate the figure after a clockwise 180° about the origin y x C D B A E C’C’ D’D’ B’B’ A’A’E’E’ Course Graphing Rotations

Try This: Example 2A An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin y x C D B A E Course Graphing Rotations

ABCDEA’B’C’D’E’ A(–6, 0)A’(0, 6) B(–5, 4)B’(4, 5) C(–3, 5)C’(5, 3) D(1, 3)D’(3, –1) Try This: Example 2A Continued E(0, 0)E’(0, 0) The new x-coordinates are the old y-coordinates. The new y-coordinates are the opposites of the old x-coordinates. Course Graphing Rotations

Try This: Example 2A Continued Rotate the figure after a clockwise 90° about the origin y x C D B A E C’C’ D’D’ B’B’ A’A’ E’E’ Course Graphing Rotations

B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin. Try This: Example 2B y x C D B A E Course Graphing Rotations

The new x-coordinates are the opposites of the old x-coordinates. The new y-coordinates are the opposites of the old y-coordinates. Try This: Example 2B Continued ABCDEA’B’C’D’E’ A(–6, 0)A’(6, 0) B(–5, 4)B’(5, –4) C(–3, 5)C’(3, –5) D(1, 3)D’(1, –3) E(0, 0)E’(0, 0) Course Graphing Rotations

Try This: Example 2B Continued Rotate the figure after a clockwise 180° about the origin y x C D B A E C’C’ D’D’ B’B’ A’A’ E’E’ Course Graphing Rotations

Lesson Quiz Give the coordinates of the vertices of the trapezoid after the given rotation. 1. Rotate trapezoid ABCD counterclockwise 180° about the origin. 2. Rotate trapezoid ABCD clockwise 90° about the origin. A’(0, 5), B’(0, 0), C’(–3, 1), D’(–3, 4) A’(5, 0), B’(0, 0), C’(1, 3), D’(4, 3) Insert Lesson Title Here Course Graphing Rotations