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Lesson Menu 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

Over Lesson 9–2 5-Minute Check 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) 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  ___

Over Lesson 9–2 5-Minute Check 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) 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  ___

Over Lesson 9–2 5-Minute Check 2 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) 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)

Over Lesson 9–2 5-Minute Check 2 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) 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)

Over Lesson 9–2 5-Minute Check 3 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) 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)

Over Lesson 9–2 5-Minute Check 3 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) 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)

Over Lesson 9–2 5-Minute Check 4 A.(x – 2, y – 3) B.(x + 2, y + 2) C.(x – 3, y + 2) D.(x + 3, y – 2) 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). ___ ____

Over Lesson 9–2 5-Minute Check 4 A.(x – 2, y – 3) B.(x + 2, y + 2) C.(x – 3, y + 2) D.(x + 3, y – 2) 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). ___ ____

Over Lesson 9–2 5-Minute Check 5 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) 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.

Over Lesson 9–2 5-Minute Check 5 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) 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.

CCSS 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.

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

Vocabulary center of rotation angle of rotation

Concept

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

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

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

Concept

Example 2 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. Use a protractor to measure a 115° angle clockwise with as one side. Use a compass to copy onto Name the segment Draw Repeat with points E and F. Draw a segment from point G to point D.

Example 2 Rotations in the Coordinate Plane Answer:

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

Example 2 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). A.B. C.D.

Example 2 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). A.B. C.D.

Example 3 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) Rotations in the Coordinate Plane

Example 3 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- and y-coordinates. (x, y) → (–y, x) (5, 3) → (–3, 5) Answer: Rotations in the Coordinate Plane

Example 3 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- and y-coordinates. (x, y) → (–y, x) (5, 3) → (–3, 5) Answer: The answer is C, (–3, 5). Rotations in the Coordinate Plane

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

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

End of the Lesson