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Dilations: Practice Name_____________________________________ Geometry section 9-5 Date_______________________Period__________ Find the image of each point under each of the following transformations. (Do all four transformations for each point.) Point (x, y) → (

1 4

x, 1 4

y) (x, y) → (x, 3y) (x, y) → (4x, 4y) (x, y) → (0.5x, 0.5y)

1. (8, 4)

2. (-12, 3)

3. (-2, 2)

4. (0, 0)

State the mapping notation for the stretching, shrinking, expansion or contraction that maps the given point into the image point shown. Also, describe the transformation, i.e. horizontal shrink, vertical stretch, etc. Mapping Mapping Notation Description

5. (5,3) → (5,6)

6. (3,2) → (6,4)

7. (10,-2) → (5,-2)

8. (8,-8) → (4,-4)

9. (-5,8) → ( 25− ,4)

10. (-6,-9) → (-4,-6)

Find the images of A(0,1), B(-3,2), C(-4,0), and D(2,-3). Draw ABCD. In another color, draw A′B′C′D′.

11. (x, y) → (2x, 2y) 12. (x, y) → (0.5x, y) 13. (x, y) → (x, 3y)

14. Graph the points A(-1,2), B(2,2), C(1,-3), and D(-2,-3). Quadrilateral ABCD is mapped to quadrilateral A′B′C′D′ under a dilation. Graph A′(-2,4), B′(4,4), C′(2,-6), and D′(-4,-6).

What kind of dilation does this represent?

What is the scale factor from ABCD to A′B′C′D′?

Describe this dilation in functional notation. 15. Given the points A(-2, 4) and B(6, 10), find:

a) slope of b) equation of ABAB c) length of AB Using the functions in the first row below and the points A and B above, fill in the table.

(x, y) → (2x, 2y) (x, y) → ( 1 2

x, 1 2

y) (x, y) → (2x, y) (x, y) → (x, 1 2

y)

Using the transformation at the top of the column find A′ & B′

A′=(_____, _____)

B′=(_____._____)

A′=(_____, _____)

B′=(_____._____)

A′=(_____, _____)

B′=(_____._____)

A′=(_____, _____)

B′=(_____._____)

Find slope of A B′ ′

How does slope of A B′ ′ com re with slope of ?

pa AB

W e the equation of

rit A B′ ′

How does th equation of compare to t equation of ?

e A B′ ′ he AB

Find A′B′

How does A′B′ compare to AB?

Transformations Review Name: ___________________________ Date: ________________ Period: _____ 1. Given A(2, -6) and B(0, 0), find

(a) length of AB __________ (b) slope of AB __________ A. translation E. 180-degree rotation I. horizontal stretching B. reflection across the x-axis F. 270-degree rotation J. horizontal shrinking C. reflection across the y-axis G. vertical stretching K. expansion D. 90-degree rotation H. vertical shrinking L. contraction For each of the transformations described in column 1, answer the questions in row 1. Show work on another sheet of paper.

Letter from list above that corresponds.

Image of A(2, -6) and B(0, 0)

Describe any fixed points.

Length of ' 'A B . Is

distance preserved?

Slope of ' 'A B . Are AB and

' 'A B || , , or neither?

⊥

Would an image triangle under this transformation be the same size and/or shape as a preimage triangle?

2. (x, y) → (x +3, y)

3. x’ = 3x, y’ = y

4. (x, y) → (-x, -y)

5. (x, y) → (x, -y)

6. x’ = 2x, y’ = 2y

7. x’ = x – 5, y’ = y + 2

8. x’ = -y, y’ = x

9. (x, y) → (y, -x)

10. x’ = -x, y’ = y

11. x’ = 0.5x, y’ = 0.5y

12. (x, y) → (x, 4y)

Letter from list below that corresponds.

Image of A(2, -6) and B(0, 0)

Describe any fixed points.

Length of ' 'A B . Is

distance preserved?

Slope of ' 'A B . Are AB and

' 'A B || , , or neither?

⊥

Would an image triangle under this transformation be the same size and/or shape as a preimage triangle?

13. x’ = ¼ x, y’ = y

14. (x, y) → (x, 1 3

y)

15. x’ = 2x + 2 y’ = 3y – 1

A. translation E. 180-degree rotation I. horizontal stretching B. reflection across the x-axis F. 270-degree rotation J. horizontal shrinking C. reflection across the y-axis G. vertical stretching K. expansion D. 90-degree rotation H. vertical shrinking L. contraction 16. Which of the transformations A-L and #2-15 have NO fixed points? 17. Triangle KMP lies entirely in quadrant I. In which quadrant will its image lie after each of these:

b) reflection across the x-axis c) reflection across the y-axis d) 90-degree rotation e) 180-degree rotation f) 270-degree rotation k) expansion l) contraction m) reflection across the line y = x

18. Vocabulary:

A transformation in which the pre-image and image are congruent is a(n) ____________________.

A transformation in which the size is different but the shape is preserved is a(n) ______________.

A composition of two reflections across two parallel lines is a(n) ____________________.

A composition of two reflections across two intersecting lines is a(n) ____________________.

19. Using the graph to the right,

________________ Find the translation rule that maps T onto T’(4,6).

__________ Find the image of S after reflecting across the y-axis.

__________ Find the image of W after reflecting across the x-axis.

__________ Find the image of V after a 90° counterclockwise rotation.

__________ Find the image of U after dilating by a scale factor of 3 1 .

20. A O P X Z C D W Which letters do not have reflectional symmetry? __________

Which letters have only 1 line of symmetry? __________

Which letters have 2 lines of symmetry? __________

Which letters do not have rotational symmetry? __________

Which letters have a 90° angle of rotation? __________

Which letters have a 180° angle of rotation? __________

Similar Figures: Proportions, Algebra, Name_______________________________ and Word Problems Date_______________________Pd_______ Find the missing variable and side lengths (if requested) for each pair of similar figures using proportions. Assume that all pairs of figures given are similar. Show all work. 2. c = ______

5. b = ______

7. q = ______

8. k = ______, m AB = ______, m AD = ______

9. j = ______

10. x = ______, m JK = ______

11. Jeremy’s house is 45 feet wide. In a photograph the width of the house was 2.5 inches, and its height was 2 inches. What is the actual height of Jeremy’s house?

12. Brandon wants to reduce a figure that is 9 inches tall and 16 inches wide so that it will fit on a 9-inch-by- 12-inch piece of paper. If he reduces the figure proportionally, what is the maximum size the reduced figure could measure?

13. Troy used chalk to outline a triangular plot of land in his backyard. The plot of land has a perimeter of 26 feet, with its longest side measuring 8 feet 10 inches. Troy wants to outline a second triangular plot of land similar to the first but with a perimeter of 42 feet. What is the measure of the longest side of the second triangular plot of land?

14. Kate has 2 similar trapezoidal pieces of paper, as shown below. Using the dimensions given, find the perimeter of trapezoid LNQS.

10q + 15

4

60

3

A

C D 8 - k

4

2

j - 6 2j - 11

4

10 10

x

5 x - 3

E F

G H

J K

L M

A ~ABCΔ DEFΔ b + 5 24 3 4 B C

D c + 5

1 2b - 5

3

4k - 2

F E

Similar Figures: Practice on the Coordinate Plane Name______________________________________________ Date ________________________________ Period ________ Two of the three figures are similar. Name the two similar figures and give the scale factor. Dashed Dotted Solid

Example 1

solid to dashed with scale factor 4 (or ratio 1:4) or dashed to solid with scale factor 4

1 (or ratio 4:1)

1. 2.

3.

4.

5.

6.

7.

8.

9. In problem 1 the dimensions of the dotted triangle are _____ times those of the solid triangle. The area of the dotted triangle is ______ times that of the solid triangle. 10. In problem 2 the dimensions of the dotted triangle are _____times those of the dashed triangle. The area of the dotted triangle is _____ times that of the dashed triangle.

Name:__________________________ Perio