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Rotations in the Coordinate Plane - Examples and Practice

This lesson focuses on rotations in the coordinate plane. It includes examples and practice problems to help students understand the concepts and apply them to different figures.

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Rotations in the Coordinate Plane - Examples and Practice

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 9–2) CCSS Then/Now New Vocabulary Key Concept: Rotation Example 1: Draw a Rotation Key Concept: Rotations in the Coordinate Plane Example 2: Rotations in the Coordinate Plane Example 3: Standardized Test Example: Rotations in the Coordinate Plane Lesson Menu

  3. Find the coordinates of the figure under the given translation.RS with endpoints R(1, –3) and S(–3, 2) along the translation vector 2, –1 ___ A.R'(–2, –2), S'(–1, 1) B.R'(0, –3), S'(–5, 3) C.R'(3, –4), S'(–1, 1) D.R'(3, –4), S'(–5, 3) 5-Minute Check 1

  4. Find the coordinates of the figure under the given translation.ΔABC with vertices A(–4, 3), B(–2, 1), and C(0, 5) under the translation (x, y) → (x + 3, y – 4) A.A'(–2, 1), B'(1, –3), C'(3, –1) B.A'(–1, –1), B'(1, –3), C'(3, 1) C.A'(0, 5), B'(–6, 3), C'(4, 7) D.A'(1, –1), B'(2, 5), C'(5, 9) 5-Minute Check 2

  5. Find the coordinates of the figure under the given translation.trapezoid LMNO with vertices L(2, 1), M(5, 1), N(1, –5) and O(0, –2) under the translation (x, y) → (x – 1, y + 4) A.L'(1, 5), M'(4, 5), N'(0, –1), O'(–1, 2) B.L'(2, 6), M'(5, 7), N'(1, 0), O'(0, 3) C.L'(3, –3), M'(6, –2), N'(0, –8), O'(–1, –6) D.L'(4, –4), M'(7, 5), N'(0, –1), O'(1, 4) 5-Minute Check 3

  6. ___ Find the translation that moves AB with endpoints A(2, 4) and B(–1, –3) to A'B' with endpoints A'(5, 2) and B'(2, –5). ____ A. (x – 2, y – 3) B. (x + 2, y + 2) C. (x – 3, y + 2) D. (x + 3, y – 2) 5-Minute Check 4

  7. The preimage of rectangle ABCD has vertices at A(–4, 5), B(–4, –3), C(1, –3), and D(1, 5). Its image has vertices at A'(–1, 3), B'(–1, –5), C'(4, –5), and D'(4, 3). Write the ordered pair that describes the transformation of the rectangle. A.(x, y) → (x + 3, y – 2) B.(x, y) → (x – 3, y + 2) C.(x, y) → (x + 2, y + 3) D.(x, y) → (x – 2, y – 3) 5-Minute Check 5

  8. Content Standards G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Mathematical Practices 2 Reason abstractly and quantitatively. 5 Use appropriate tools strategically. CCSS

  9. You identified rotations and verified them as congruence transformations. • Draw rotations. • Draw rotations in the coordinate plane. Then/Now

  10. center of rotation • angle of rotation Vocabulary

  11. Concept

  12. Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR. Draw a Rotation Rotate quadrilateral RSTV45° counterclockwise about point A. • Draw a segment from point R to point A. • Locate point R' so that AR = AR'. • Repeat this process for points S, T, and V. • Connect the four points to form R'S'T'V'. Example 1

  13. Draw a Rotation Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A. Answer: Example 1

  14. For the diagram, which description best identifies the rotation of triangle ABC around point Q? A. 20° clockwise B. 20° counterclockwise C. 90° clockwise D. 90° counterclockwise Example 1

  15. Concept

  16. Use a protractor to measure a 115° angle clockwise with as one side. Draw Use a compass to copy onto Name the segment Rotations in the Coordinate Plane Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 115° clockwise about the point G(–4, –2). First, draw ΔDEF and plot point G. Draw a segment from point G to point D. Repeat with points E and F. Example 2

  17. Rotations in the Coordinate Plane Answer: ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G. Example 2

  18. A.B. C. D. Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1). Example 2

  19. Rotations in the Coordinate Plane Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin? A (5, –3) B (–5, –3) C (–3, 5) D (3, –5) Example 3

  20. Rotations in the Coordinate Plane Read the Test Item You are given a graph of hexagon DGJTSR and asked to identify the coordinates of the image of point T after a 90° counterclockwise rotation about the origin. Solve the Test Item To find the coordinates of point T after a 90counterclockwise rotation about the origin, multiply the y-coordinate by –1 and then interchange the x- andy-coordinates. (x, y) → (–y, x) (5, 3) →(–3, 5) Answer: The answer is C, (–3, 5). Example 3

  21. Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin? A. (–5, –4) B. (–5, 4) C. (5, 4) D. (4, –5) Example 3

  22. End of the Lesson

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