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NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Course 3 • Chapter 6 Transformations 89

Lesson 1 Homework Practice Translations Draw the image of the figure after the indicated translation. 1. 3 units right and 2 units up 2. 5 units right and 3 units down 3. 2 units left and 1 unit up 4. 4 units left and 2 units down Graph the figure with the given vertices. Then graph the image of the figure after the indicated translation, and write the coordinates of its vertices. 5. ∆FGH with vertices F(1, 3), G(2, 4), and H(3, 2); translated 3 units left and 1 unit down

6. rectangle PQRS with vertices P(–4,–1), Q(0, 1), R(1,–1), and S(–3,–3) translated 2 units right and 3 units up

7. QUILTS The quilt design at the right is a traditional

American design. Describe the minimum number of translations of the original pattern, A, needed to create the section shown.

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Course 3 • Chapter 6 Transformations 91

Lesson 2 Homework Practice

Reflections

1. Graph ∆ABC with vertices A(2, 2),

B(5, 4),and C(5, 1) and its reflection

over the x-axis. Then find the

coordinates of the reflected image.

2. Graph square ABCD with vertices

A(–1, 2), B(2, –1), C(5, 2), and D(2, 5)

and its reflection over the y-axis. Then

find the coordinates of the reflected image.

The coordinates of a point and its image after a reflection are given. Describe the reflection as over the x-axis or y-

axis.

3. B(1, –2) → Bʹ(1, 2) 4. J(–3, 5) → Jʹ(–3, –5) 5. W(–7, –4) → Wʹ(7, –4)

For Exercises 6–9, use the following information.

Triangle XYZ has vertices X(4, 2), Y(4, 4), and Z(0, 2).

6. What are the coordinates of the image of point X

after a reflection over the y-axis?

7. What are the coordinates of the image of point Y

after a reflection over the y-axis?

8. What are the coordinates of the image of point Z

after a reflection over the y-axis?

9. Graph triangle XYZ and its image after a reflection over the x-axis.

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Course 3 • Chapter 6 Transformations 95

Lesson 3 Homework Practice

Rotations

For Exercises 1 and 2, graph quadrilateral EFGH and its image after each rotation. Then give the coordinates of

the vertices for quadrilateral EʹFʹGʹHʹ.

1. 90° clockwise about vertex H

2. 180° counterclockwise about vertex E

3. Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).

Graph the figure and its rotated image after a clockwise

rotation of 180° about the origin. Then give the coordinates

of the vertices for triangle RʹSʹTʹ.

4. Quadrilateral KLMN has vertices K(2, 0), L(4, 0), M(5, –2),

and N(1, –2). Graph the figure and its rotated image after a

counterclockwise rotation of 90° about the origin. Then give

the coordinates of the vertices for quadrilateral KʹLʹMʹNʹ.

Course 3 • Chapter 6 Transformations 97

Lesson 4 Homework Practice

Dilations

Find the coordinates of the vertices of each figure after a dilation with the given scale factor k. Then graph the

original image and the dilation.

1. S(–2, 1), U(0, 1), N(–1, –1); k = 4 2. M(–3, 1), A(1, 3), T(2, –2), H(–4, –2); k

3. F(–2, 1), U(–1, 2), N(3, 1); k = 2 4. P(–4, 2), L(2, 4), A(2, –4), Y(–4, –2); k

5. MAPS Rachel and her cousin, Lena, live in different cities that are about 100 miles apart. On a map, the two cities

measure 5 inches apart. What is the scale factor used for the map?

6. GEOMETRY A square has vertices J(–1, 4), U(5, 4), M(5, –2), P(–1, –2). After a dilation, square JUMP has vertices

J(–0.5, 2), U(2.5, 2), M(2.5, –1), P(–0.5, –1). What is the scale factor of the dilation?

7. LANDSCAPING A landscape designer has a drawing of a flower bed that measures 6 inches by 9 inches. The owner

wants the actual flower bed to be 5 feet by 7.5 feet. What is the scale factor the designer must use to install the new

flower bed?

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