Review for Chapter 8 Test Transformations

Name: ________________________ Class: ___________________ Date: __________
ID: A
Transformations Review 2015
Short Answer
The shaded figure is congruent to the nonshaded figure. Describe two different sequences of
transformations in which the nonshaded figure is the image of the shaded figure.
1.
2. The vertices of a rectangle are W ÊÁË 2,2ˆ˜¯ , X ÊÁË 4,3 ˆ˜¯ , Y ÊÁË 5,2 ˆ˜¯ , and Z ÊÁË 4,1 ˆ˜¯ . Reflect the figure in the y-axis, and
then translate the image 3 units right and 4 units down. What are the coordinates of the image?
3. The vertices of a rectangle are A ÁÊË 2,0 ˜ˆ¯ , B ÁÊË 5,0 ˜ˆ¯ , C ÁÊË 5,−2˜ˆ¯ , and D ÁÊË 2,−2 ˜ˆ¯ Reflect the rectangle in the y-axis,
and then rotate the rectangle 180° about the origin. What are the coordinates of the image?
4. The vertices of a triangle are X ÊÁË −6,−9ˆ˜¯ , Y ÊÁË −3,−9 ˆ˜¯ , and Z ÊÁË −3,3 ˆ˜¯ . Dilate the triangle with respect to the
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origin using a scale factor of Then reflect the triangle in the x-axis. What are the coordinates of the image?
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5. Explain how you know if a dilation is an enlargement or a reduction.
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Name: ________________________
ID: A
6. Translate the triangle 2 units right and 2 units down. Then reflect the image in the y-axis.
The vertices of a parallelogram are D(–5, 3), E(–7, 6), F(–3, 6), and G(–1, 3). Rotate the parallelogram
as described. Find the coordinates of the image.
7. 180° clockwise about vertex G
8. 90° counterclockwise about vertex E
9. The red figure represents the starting position of table and the blue figure represents the new position after it
has been moved. Describe two different sequences of transformations in which the blue table is the image of
the red table.
10. You rotate a triangle 90° clockwise about the origin. Then you translate its image down 5 units and
left 5 units. Finally, you reflect the image over the y -axis. The vertices of the final image are (5,− 2), (7,− 4),
(2,− 4). What are the vertices of the original triangle?
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Name: ________________________
ID: A
Essay
11. Three triangular gardens are being planned for a new park. Sergio has placed his plans on a coordinate plane
to help him determine the locations for the gardens. The diagram shows the location of the first garden
named ∆FLO.
a. First, Sergio reflects ∆FLO over the line y = x to form the second garden ∆F ′L ′O ′ . Copy the diagram and
draw ∆F ′L ′O ′ . Describe how the coordinates for ∆FLO relate to the coordinates for ∆F ′L ′O ′ .
b. Next, Sergio reflects ∆F ′L ′O ′ over the x-axis to form the third garden ∆F ″L ″O ″. Draw ∆F ″L ″O ″ on your
drawing for part a. Describe how the coordinates for ∆F ′L ′O ′ relate to the coordinates for ∆F ″L ″O ″.
c. Can you name a rotation that would move ∆FLO to ∆F ″L ″O ″. If so, what is the angle of rotation?
Other
12. Application Similar figures can be formed using algebraic rules to transform coordinates.
a. Five algebraic rules are listed in the table below.
1
(x, y) → (3x + 3, − 3y)
2
(x, y) → (−x − 1,y + 1)
3
(x, y) → (0.5x,− 0.5y − 5)
4
(x, y) → (−2y + 5,2x − 3)
5
(x, y) → (−3x − 4,− 4y + 2)
a. Choose two of the algebraic rules above, explain how every part of the rule transforms the original
triangle?
b. Choose a third rule and apply it to the following triangle: A( 1, 2 ) B( -3, 4 ) C ( -1, -2 )
List the coordinates for A', B', C'
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Name: ________________________
ID: A
13. Extended Response A figure is congruent to another figure if you can create the second figure from the
first by a sequence of translations, reflections, and rotations.
a. Is triangle GH J congruent to triangle KLM ? Explain your reasoning.
b. Is triangle GH J congruent to triangle NPQ? Explain your reasoning.
14. Extended Response A figure is similar to another figure if you can create the second figure from the first
by a sequence of translations, reflections, rotations, and dilations.
a. Is triangle H J K congruent to triangle LM N? Explain your reasoning.
b. Is triangle H J K similar to triangle PQR? Explain your reasoning.
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Name: ________________________
ID: A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 15. Use arrow notation to write a rule that describes the translation of a point from (–4, –2) to (–1, –1).
c. (x, y) → (x − 3, y + 1)
a. (x, y) → (x + 3, y − 1)
b. (x, y) → (x + 3, y + 1)
d. (x, y) → (x − 3, y − 1)
____ 16. ∆PQR has vertices P(1, –2), Q(7, –3), and R(–3, –8). The triangle is translated left 6 units and down 3 units.
Without graphing, find the coordinates of P ′, Q ′, and R ′.
a. P ′(–5, 1), Q ′(1, 0), R ′(–9, –5)
c. P ′(–5, –5), Q ′(1, –6), R ′(–9, –11)
b. P ′(7, –5), Q ′(13, –6), R ′(3, –11)
d. P ′(7, 1), Q ′(13, 0), R ′(3, –5)
____ 17. Use arrow notation to write a rule that describes the translation shown on the graph.
a.
b.
(x, y) → (x + 3, y − 4)
(x, y) → (x + 3, y + 4)
c.
d.
(x, y) → (x − 3, y − 4)
(x, y) → (x − 3, y + 4)
____ 18. Point A(8, –4) is reflected over the x-axis. Write the coordinates of A′.
a. (–8, 4)
b. (–8, –4)
c. (8, –4)
d.
(8, 4)
____ 19. What are the coordinates of the point H(–1, –2) after a rotation of 180° about the origin?
a. (–2, 1)
b. (2, –1)
c. (1, 2)
d. (–1, 2)
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Name: ________________________
ID: A
Find the coordinates of the image after the transformation.
____ 20. Rotate 90° clockwise about the origin.
a.
b.
c.
d.
F'(6, –2), G'(6, –5), H '(1, –4), J '(1, –1)
F'(–6, –2), G'(–6, –5), H'(–1, –4), J '(–1, –1)
F'(–6, 2), G'(–6, 5), H '(–1, 4), J '(–1, 1)
F'(–2, –6), G'(–5, –6), H'(–4, –1), J '(–1, –1)
____ 21. Rotate 180° about the origin.
a.
b.
c.
d.
K'(2, 4), L'(6, 5), M '(6, 2), N'(2, 1)
K'(4, –2), L'(5, –6), M '(2, –6), N'(1, –2)
K'(–2, –4), L'(–6, –5), M '(–6, –2), N'(–2, –1)
K'(–2, 4), L'(–6, 5), M '(–6, 2), N'(–2, 1)
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Name: ________________________
____ 22. Dilate with a scale factor of
a.
b.
ID: A
1
.
3
F'(15, 6), G'(15, 11), H'(30, 6)
5
5 11
10
F'( , 2), G'( , ), H'( , 2)
3
3 3
3
c.
F'(5, 6), G'(5, 11), H'(10,6 )
d.
F'(15, 18), G'(15, 33), H'(30, 18)
c.
T'(6, 1), V'(6, 3), W'(12, 1)
d.
T'(6, 3), V'(6, 9), W'(12, 3)
____ 23. Dilate with a scale factor of 3.
a.
b.
2 1
2
4 1
T'( , ), V'( , 1), W'( , )
3 3
3
3 3
T'(2, 1), V'(2, 3), W'(4,1 )
Find the coordinates of the figure after reflecting in the x-axis.
____ 24. G(1, –4), H (8, –4), J (7, –5), K(0, –7)
a. G'(1, –4), H'(8, –4), J'(7, –5), K'(0, –7)
b. G'(1, 4), H'(8, 4), J'(7, 5), K'(0, 7)
c. G'(–1, 4), H'(–8, 4), J'(–7, 5), K'(–0, 7)
d. G'(–1, –4), H'(–8, –4), J'(–7, –5), K'(–0, –7)
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Name: ________________________
ID: A
____ 25. The coordinates below represent the dimensions of a room on a building blueprint. To make the room fit the
needs of the owner, the builder needs to make changes. Reflect in the x-axis. Then dilate with respect to the
1
origin using a scale factor of .
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A ÊÁË −5,−5ˆ˜¯ , B ÊÁË −5,0 ˆ˜¯ , C ÊÁË 1,0 ˆ˜¯ , D ÊÁË 1,−5 ˆ˜¯
a. A″ ÊÁË −4.5,5.5 ˆ˜¯ , B ″ ÊÁË −4.5,5.5 ˆ˜¯ , C ″ ÊÁË 1.5,0.5 ˆ˜¯ , D ″ ÊÁË 1.5,5.5 ˆ˜¯
b. A″ ÊÁË 5.5,−4.5 ˆ˜¯ , B ″ ÊÁË 5.5,0.5 ˆ˜¯ , C ″ ÊÁË −0.5,0.5 ˆ˜¯ , D ″ ÊÁË −0.5,−4.5 ˆ˜¯
c. A″ ÊÁË −2.5,2.5 ˆ˜¯ , B ″ ÊÁË −2.5,0 ˆ˜¯ , C ″ ÊÁË 0.5,0 ˆ˜¯ , D ″ ÊÁË 0.5,2.5 ˆ˜¯
d. A″ ÊÁË 2.5,−2.5 ˆ˜¯ , B ″ ÊÁË 2.5,0 ˆ˜¯ , C ″ ÊÁË −0.5,0 ˆ˜¯ , D ″ ÊÁË −0.5,−2.5 ˆ˜¯
____ 26. Which translation below is NOT described by the rule
a. (3, –2)
(5, –5)
c. (0, 4)
b. (–4, 1)
(–2, –2)
d. (1, –5)
?
(2, 1)
(3, –2)
____ 27.
Given
a.
b.
c.
d.
DEF ≅
D' E' F' , describe a sequence of rigid motions that maps
DEF to
D' E' F' .
reflection across the y-axis, reflection across the x-axis, translation of 4 units left
translation of 5 units down, translation of 4 units right, reflection across the y-axis
rotation of 90° about the origin, translation of 5 units down, translation of 4 units left
reflection across the x-axis, translation of 4 units left, translation of 5 units up
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Name: ________________________
ID: A
____ 28.
Is
DEF ≅
D' E' F' ?
Choose the best explaination.
a.
b.
c.
d.
Yes, because a reflection across the x-axis, followed by a translation of 6 units left and 3
units up, maps DEF to D' E' F' .
Yes, because reflections across the y-axis and the x-axis, followed by a translation of 6
units left, map DEF to D' E' F' .
Yes, because a translation of 3 units down and 6 units right, followed by a reflection
across the y-axis, maps DEF to D' E' F' .
No, because a sequence of rigid motions does not map DEF to D' E' F' .
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