Five-Minute Check (over Lesson 9–2)

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

Over Lesson 9–2

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

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Over Lesson 9–2

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

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

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).

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Over Lesson 9–2

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.

You identified rotations and verified them as congruence transformations. (Lesson 4–7)

• Draw rotations.

• Draw rotations in the coordinate plane.

• center of rotation

• angle of rotation

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'.

Draw a Rotation

Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A.

Answer:

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?

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.

Rotations in the Coordinate Plane

Answer: ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G.

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.

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)

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 90counterclockwise 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).

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?