Transformations Unit Review

Transformations – Unit Review 1. For each transformation in the table below, indicate which properties are true by placing a check mark in every appropriate box.

The image and The image and Lengths of Measures of preimage are preimage are segments are angles are similar but not congruent preserved preserved congruent Translation

Reflection

Rotation Glide Reflection Dilation

2. Identify the rigid motion that maps the figure on the right onto the figure on the left. a. b.

3. ∆R’S’T’ is a translation image of ∆RST. What is a rule for the translation?

4. Find the coordinates of the vertices of each image.

a. Rx-axis(ABCD) b. Ry-axis(ABCD)

c. Ry=x(ABCD) d. Ry=2 (ABCD)

Geometry – Transformations ~1~ NJCTL.org e. Rx=-1(ABCD) f. r(270°, O)(ABCD)

g. r(180°, O)(ABCD) h. r(90°, O)(ABCD)

i. D5(ABCD) j. T<2, -5> (ABCD)

k. (Ry = -2 ○ T<-4, 0>)(ABCD)

5. Draw the line of reflection you can use to map one figure onto the other.

6. Find the image of M(-1, 4) after two reflections, first across line ℓ1, and then across line ℓ2.

a. ℓ1 : x = 2, ℓ2 : y-axis b. ℓ1 : y = –2, ℓ2 : x-axis

7. The letter H is reflected across the line x = -2 and then line x = 4. Describe the resulting transformation.

8. The letter J is reflected across line m and then line n. Describe the resulting transformation.

Geometry – Transformations ~2~ NJCTL.org 9. Point K is the center of regular quadrilateral ABCD. Find the image of the given point or segment for the given rotation. (counterclockwise) a. r(90°, K)(K)

b. r(270°, K)(N)

c. r(180°, K)(ML)

d. r(360°, K)(JN)

e. r(90°, K)(JO)

10. Graph ∆ABC and its glide reflection image. A(-5, 3), B(1, 2) and C(-2,-4)

a. (RX-axis ○ T<2, 1>)(∆ABC) 4.(Ry=2 ○ T<–1, 0>)(∆ABC)

Geometry – Transformations ~3~ NJCTL.org 11. Write a congruence statement for the two figures in the coordinate grid. Then write a congruence transformation that maps one figure to the other.

12. Write a similarity statement for the two figures in the coordinate grid. Then write a similarity transformation that maps one figure to the other.

13. The solid-line figure is a dilation of the dashed-line figure with center of dilation P. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?

14. A dilation has center (0, 0). Find the image of each point for the given scale factor.

Geometry – Transformations ~4~ NJCTL.org a. P(-2, 4); D4(P) b. A(10, 4); D1/4(A) c. K(3, -6); D0.5(K)

15. Does the figure have reflectional symmetry? If so draw the line(s) of symmetry. Does the figure have rotational symmetry? If so state the degree of rotation.

16. Draw the image of the figure for the given rotation about P. Use prime notation to label the vertices of the image.

r(100°, P)(∆ABC)

Geometry – Transformations ~5~ NJCTL.org ANSWER KEY Transformations – Unit Review 1. For each transformation in the table below, indicate which properties are true by placing a check mark in every appropriate box.

The image and The image and Lengths of Measures of preimage are preimage are segments are angles are similar but not congruent preserved preserved congruent Translation X X X

Reflection X X X

Rotation X X X Glide X X X Reflection Dilation X X

2. Identify the rigid motion that maps the figure on the right onto the figure on the left. a. b.

Rotation Reflection

3. ∆R’S’T’ is a translation image of ∆RST. What is a rule for the translation?

T<-7, 3>(∆RST) = ∆R’S’T’

4. Find the coordinates of the vertices of each image.

a. Rx-axis(ABCD) b. Ry-axis(ABCD)

A(-4, -3), B(1, -6), C(4, -5), D(0, -2) A(4, 3), B(-1, 6), C(-4, 5), D(0, 2)

c. Ry=x(ABCD) d. Ry=2 (ABCD)

A(3, -4), B(6,1), C(5, 4), D(2, 0) A(-4, 1), B(1, -2), C(4, -1), D(0, 2)

e. Rx=-1(ABCD) f. r(270°, O)(ABCD)

Geometry – Transformations ~6~ NJCTL.org A(2, 3), B(-3, 6), C(-6, 5), D(1, 2) A(-3, -4), B(-6, 1), C(-5, 4), D(-2, 0)

g. r(180°, O)(ABCD) h. r(90°, O)(ABCD)

A(4, -3), B(-1, -6), C(-4, -5), D(0, -2) A(3, 4), B(6, -1), C(5, -4), D(2, 0)

i. D5(ABCD) j. T<2, -5> (ABCD)

A(-20, 15), B(5, 30), C(20, 25), D(0, 10 A(-2, -2), B(2, 1), C(6, 0), D(2, -3)

k. (Ry = -2 ○ T<-4, 0>)(ABCD)

A(-8, -7), B(-3, -10), C(0, -9), D(-4, -6)

5. Draw the line of reflection you can use to map one figure onto the other.

6. Find the image of M(-1, 4) after two reflections, first across line ℓ1, and then across line ℓ2.

a. ℓ1 : x = 2, ℓ2 : y-axis b. ℓ1 : y = –2, ℓ2 : x-axis

(-5, 4) (-1, 8)

7. The letter H is reflected across the line x = -2 and then line x = 4. Describe the resulting transformation. A translation 12 units to the right.

8. The letter J is reflected across line m and then line n. Describe the resulting transformation. 150 degree rotation clockwise

Geometry – Transformations ~7~ NJCTL.org 9. Point K is the center of regular quadrilateral ABCD. Find the image of the given point or segment for the given rotation. (counterclockwise) a. r(90°, K)(A) D

b. r(270°, K)(D) A

c. r(180°, K)(DC) AB

d. r(360°, K)(KB) KB

e. r(90°, K)(BC) AB

10. Graph ∆ABC and its glide reflection image. A(-5, 3), B(1, 2) and C(-2,-4)

a. (RX-axis ○ T<2, 1>)(∆ABC) 4.(Ry=2 ○ T<–1, 0>)(∆ABC)

11. Write a congruence statement for the two figures in the coordinate grid. Then write a congruence transformation that maps one figure to the other.

∆ABC ≅ ∆FGH;

Sample: Rx-axis○ T<3, -1>(∆ABC) = ∆FGH

Geometry – Transformations ~8~ NJCTL.org 12. Write a similarity statement for the two figures in the coordinate grid. Then write a similarity transformation that maps one figure to the other.

∆TUV ~ ∆XYZ; Sample: T<-4, -3> ○D2(∆TUV) = ∆XYZ

13. The solid-line figure is a dilation of the dashed-line figure with center of dilation P. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?

enlargement; 7/4

14. A dilation has center (0, 0). Find the image of each point for the given scale factor.

a. P(-2, 4); D4(P) b. A(10, 4); D1/4(A) c. K(3, -6); D0.5(K)

(-8, 16) (5/2, 1) (1.5, -3)

15. Does the figure have reflectional symmetry? If so draw the line(s) of symmetry. Does the figure have rotational symmetry? If so state the degree of rotation.

180 degree rotational symmetry

16. Draw the image of the figure for the given rotation about P. Use prime notation to label the vertices of the image.

r(100°, P)(∆ABC)

Geometry – Transformations ~9~ NJCTL.org