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Transformations Study Guide

Total questions: 100

Worksheet time: 4hrs 38mins

Name
Class
Date
1.

Point H is located at (-7, 5).

Where is H’ after a 270° clockwise rotation?

a)

(-5, -7)

b)

(7, -5)

c)

(5, 7)

d)

(-7, 5)

2.

Point R is located at (8, 13).

Where is R’ after a translation 8 units left and 6 units down?

a)

(8, 13)

b)

(0, 7)

c)

(18,19)

3.

Point L is located at (-3,-6).

Where is L’ after a reflection over the y-axis?

a)

(6, 3)

b)

(3, 6)

c)

(3, -6)

4.

What is correct algebraic representation of a Rotation 180° clockwise.

a)

(-x, -y)

b)

(x, -y)

c)

(-x, y)

d)

(y, -x)

5.

Describe the transformation that occurred.

a)

Rotation 90° C/270° CC

b)

Translation 8 left 2 down

c)

Dilation; SF 1/3

d)

Rotation 270° C/90° CC

6.

Describe the transformation that occurred.

a)

Rotation 90° C/270° CC

b)

Translation 8 left 2 down

c)

Dilation; SF 1/3

d)

Translation 8 right 2 up

7.
A turn is also called a ___________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
8.

Identify the transformation.

a)

Reflection across y-axis

b)

Reflection across x-axis

c)

Translation

d)

Rotation

9.
A slide is also called a _________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
10.
Identify the transformation from ABCD to A'B'C'D'.
a)
Translation
b)
Reflection across the y-axis
c)
Reflection across the x-axis
d)
90o counter clockwise Rotation
11.
The image shows what type of transformation
a)
Rotation
b)
Translation
c)
Reflection
12.
Is the picture being reflected in the y-axis or x-axis?
a)
y-axis
b)
x-axis
13.
How is triangle ABC being translated to triangle A'B'C'?
a)
up 3, left 8
b)
up 9, left 4
c)
down 3, right 8
d)
down 9, right 4
14.
 Describe the Transformation
a)
Translation
b)
Rotation
c)
Reflection
15.
If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?
a)
(-5, 5)
b)
(-3, 5)
c)
(-5, 3)
d)
(-3, 3)
16.

Determine where X' would be if you translated the figure -3 units to the horizontally and -9 units vertically.

a)

(-4, 4)

b)

(-10, 2)

c)

(-4, -5)

d)

(-1, 5)

17.

Which transformation is shown?

a)

Translation

b)

Reflection over the x-axis

c)

Reflection over the y-axis

d)

90o clockwise rotation

18.

Which transformation is shown?

a)

Translation

b)

Reflection over the x-axis

c)

Reflection over the y-axis

d)

90o counterclockwise rotation

19.

Which transformation is shown?

a)

Translation

b)

Reflection over the x-axis

c)

Reflection over the y-axis

d)

180o rotation

20.

Which transformation is shown?

a)

Translation

b)

Reflection over the x-axis

c)

Reflection over the y-axis

d)

180o rotation

21.

What sequence of transformations could map ∆ABC onto its image ∆A''B''C''?

a)

a reflection followed by a rotation

b)

a reflection followed by a translation

c)

a translation followed by a rotation

d)

a translation followed by a reflection

22.

Which of the following describes the sequence of transformations shown?

a)

Reflect across the x-axis and then rotate -90 degrees cw around the origin

b)

Rotate 90 degrees cw around the origin and then translate down.

c)

Reflect across the x-axis and then reflect across the y-axis.

d)

Translate up and then rotate 90 degrees ccw about the origin.

23.
What is the sequence of transformations?
a)
Reflect over the y then reflect over the x
b)
Reflect over the x then reflect over the y
c)
Translate 4 units then rotate 90˚
d)
Rotate 90˚ then reflect over the x
24.

Which series of transformations were performed in the figure?

a)

Translation 5 units down, reflection over the y-axis

b)

Reflection over the x-axis, translation 6 units right

c)

Rotation 90o clockwise, reflection over the x-axis

d)

Rotation 180o clockwise, reflection over the y-axis

25.
Describe a sequence of transformations that maps figure A onto figure B.
a)
A translation 4 units right followed by a reflection across the x-axis
b)
A reflection across the x-axis followed by a reflection across the y-axis
c)
A reflection across the y-axis followed by a translation 6 units down
d)
A 90° counter-clockwise rotation about the Origin followed by a reflection across the y-axis
26.
Triangle ABC is rotated 180 degrees clockwise around the origin and reflected over the y-axis. What is the quadrant of the final image?
a)
I
b)
II
c)
III
d)
IV
27.

What is the correct algebraic representation of a Dilation with a Scale Factor of 2.

a)

(2x, 2y)

b)

(x+2, y+2)

c)

(x – 2, y + 2)

d)

(1/2x, 1/2y)

28.

Point B is located at (4,-16).

Where is B’ after a dilation with a scale factor of 3/4?

a)

(3, -12)

b)

(4, -16)

c)

(3, 12)

29.

What is the correct algebraic representation of a Translation 2 right and 2 down.

a)

(2x, -2y)

b)

(x + 2, y – 2)

c)

(x – 2, y + 2)

d)

(1/2x, 1/2y)

30.

What is the correct algebraic representation of a Reflection over the y-axis.

a)

(x, -y)

b)

(-x, y)

c)

(-x, -y)

d)

(x, y)

31.

Point J(-3, -7) was rotated to J’(7, -3). How many degrees was the rotation? Select all that apply.

a)

90° clockwise

b)

90° counterclockwise

c)

270° clockwise

d)

270° counterclockwise

e)

180° clockwise

32.

Point M(2, 4) was dilated to M’(9, 18). What was the scale factor, and was the dilation an enlargement or reduction?

a)

Scale Factor: 9/2

Enlargement

b)

Scale Factor: 9/2

Reduction

c)

Scale Factor: 2/9

Enlargement

d)

Scale Factor: 2/9

Enlargement

33.

Describe the transformation that occurred.

a)

Rotation 90° C/270° CC

b)

Translation 8 left 2 down

c)

Dilation; SF 1/3

d)

Dilation; SF 3

34.

Give an algebraic representation of the transformation.

a)

(-x, -y)

b)

(y, -y)

c)

(1/3x, 1/3y)

d)

(3x, 3y)

35.

Describe the transformation that occurred by using the coordinates.

A(-6, -2) → A’(-6, 2)

B(-3, -6) → B’(-3, 6)

C(-2, -2) → C’(-2, 2)

a)

Reflection over x-axis

b)

Reflection over y-axis

c)

Rotation 270° clockwise

or 90° counterclockwise

d)

Rotation 90° clockwise

or 270° counterclockwise

36.

Describe the transformation that occurred by using the coordinates.

G(-2, 7) → G’(-7, -2)

H(-4, 8) → H’(-8, -4)

I(-3, 5) → I’(-5, -3)

a)

Reflection over x-axis

b)

Reflection over y-axis

c)

Rotation 270° clockwise

or 90° counterclockwise

d)

Rotation 90° clockwise

or 270° counterclockwise

37.

Describe the transformation that occurred by using the coordinates.

J(11, -8) → J’(1, -5)

K(6, -1) → K’(-4, 2)

L(3, -7) → L’(-7, -4)

a)

Translation 10 right and 3 up

b)

Translation 10 left and 3 up

c)

Translation 10 left and 3 down

d)

Translation 10 right and 3 down

38.

Describe the transformation that occurred by using the coordinates.

D(15, 10) → D’(6, 4)

E(5, 10) → E’(2, 4)

F(10, -5) → F’(4, -2)

a)

Dilation; SF = 5/2

b)

Dilation; SF = 2/5

c)

Rotation 270° clockwise

d)

Dilation; SF = 5

39.

(0.2x, 0.2y)

a)

Reduction

b)

Enlargement

40.

(4/5x, 4/5y)

a)

Reduction

b)

Enlargement

41.

(5/4x, 5/4y)

a)

Reduction

b)

Enlargement

42.

(7.5x, 7.5y)

a)

Reduction

b)

Enlargement

43.

Describe the two transformations that occurred.

a)

Reflection over y-axis then Dilation; SF = 2/3

b)

Reflection over x-axis then Translation 9 right 1 up

c)

Rotation 180° then Reflection over y-axis

44.

Translations, reflections and rotations are all known as ________________________.

a)

Geometry

b)

Transformations

c)

Congruent

45.
A turn is also called a ___________.
a)
Translation
b)
Reflection
c)
Rotation
d)
Transformation
46.
Reflections over the x-axis change the ____-__________. 
a)
y-coordinate
b)
x-coordinate
47.
Triangle GHI is reflected across the x-axis.  What are the coordinates of I'?
a)
(-2, 6)
b)
(2, 6)
c)
(-6, -2)
d)
(6, 2)
48.
What is this picture an example of? 
a)
An angle
b)
A cat vertex 
c)
Rotation 
d)
Dilation
49.
Translation are always _______
a)
Congruent
b)
Bigger
c)
Smaller
d)
Rotated
50.
What is a reflection?
a)
When you turn an object around a point.
b)
When you slide an object form one place to another.
c)
When you flip or mirror an object across a line.
d)
When you resize an object.
51.
A type of transformation where a geometric figure slides horizontally, vertically, or both. What type of transformation is this? 
a)
dilation
b)
translation
c)
rotation
d)
reflection
52.

How many units and in which direction were the x-coordinates of parallelogram ABCD moved?

a)

3 units to the right

b)

3 units to the left

c)

7 units to the right

d)

7 units to the left

53.

Which image shows the original transformed by a reflection?

a)
b)
c)
d)
54.

They transform it by rotating the triangle shown above 90 degreesclockwise about the origin. What does the new design look like?

a)
b)
c)
d)
55.

Which of the following is a single reflection of figure N over the y-axis to form N'?

a)
b)
c)
d)
56.

Figure EFGH in the coordinate plane has vertices at (-5,2), (-5,-2), (-1,-2), and (-1,2).

If the figure is translated 5 units to the right and 2 units up, what are the coordinates of the E'F'G'H'?

a)
b)
c)
d)
57.

The shaded piece has been transformed into a frieze pattern.

Which transformations best describe how the pattern was created?

a)

reflections

b)

translations

c)

reflections and rotations

d)

translations and rotations

58.

Which of the following transformations does NOT change the shape or size of a figure? Check ALL that apply.

a)

rotation

b)

translation

c)

reflection

d)

dilation

59.

If a polygon is translated, which of the following

characteristics of the polygon are the same? Check ALL that apply.

a)

side lengths

b)

area

c)

perimeter

d)

coordinates

60.

If trapezoid KLMN shown below is reflected across the x-axis to form trapezoid K'L'M'N', what are the apparent coordinates of M'?

a)

(-4,5)

b)

(-4,-5)

c)

(4, -5)

d)

(4, 5)

61.

Which of the following can change the dimensions (size) of a figure?

a)

translation

b)

dilation

c)

reflection

d)

rotation

62.

What are the coordinates of P' when triangle PQR is dilated by a scale factor of 3 using the origin as the center?

a)

(6,8)

b)

(3, 23)\left(3,\ \frac{2}{3}\right)

c)

(23, 3)\left(\frac{2}{3},\ 3\right)

d)

(18,6)

63.

A polygon has been rotated about the origin.

Which statement must be true?

a)

The lengths of the sides are doubled.

b)

The area of the polygon did not change.

c)

The coordinates of the vertices did not change.

d)

The area of the polygon is 4 times its original area.

64.

Which set of transformations will

always produce a congruent shape?

a)

dilation, rotation, translation

b)

reflection, dilation, translation

c)

rotation, reflection, dilation

d)

rotation, translation, reflection

65.

If triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A'?

a)

(-5,-4)

b)

(-5,4)

c)

(-4,5)

d)

(-4,-5)

66.

Trapezoid ABCD below is to be translated to trapezoid A'B'C'D' by the following motion rule.
 (x,y)→(x+3, y−4)(x,y)→(x+3,\ y-4)  

What will be the coordinates of vertex C'?

a)

(1,-3)

b)

(2,1)

c)

(6,1)

d)

(8,-3)

67.

Which expression describes the translation of point from

(-3, 4) to (4,-1)

a)

7 units left and 5 units up

b)

7 units right and 5 units up

c)

7 units left and 5 units down

d)

7 units right and 5 units down

68.

Triangle DEF is reflected on the y-axis to form triangle D'E'F', what is the relationship of the coordinates of triangle DEF and triangle D'E'F' ?

a)

The x-coordinates are the same on both

triangles while the y-coordinates are opposites.

b)

The x-coordinate and the y-coordinates are

equal to each other in the triangles.

c)

The y-coordinates are the same on both triangles while the

x-coordinates are opposites.

d)

There is no relationship between the coordinates

69.

A dilation of scale factor 2 is applied to rectangle ABCD, centered at the origin. What are the coordinates of B'?

a)

(1,2)

b)

(2,1)

c)

(4,8)

d)

(8,4)

70.

Unit 1

Figure 1 is transformed as shown in the diagram, resulting in Figure 3. What are the transformations?

a)

Dilation, then reflection

b)

Rotation, then translation

c)

Reflection, then translation

d)

Translation, then reflection

71.

Unit 1

In this diagram, where is the line of reflection

a)

y=-1

b)

x=1

c)

x=-1

d)

y=1

72.

Is the result of the dilation a Enlargement or a Reduction?

a)

Enlargement

b)

Reduction

73.
Point C (-5, 4) is reflected over the x-axis. What are the coordinates of C'? 
a)
(5, 4)
b)
(-5, -4)
c)
(5, -4)
d)
(-5, 4) 
74.
Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)
a)
A'(9,9) B'(18,18) C'(27,9)
b)
A'(6,6) B'(9,9) C'(12,6)
c)
A'(0,0) B'(3,3) C'(6,0)
d)
A'(1,1) B'(2,2) C'(3,1)
75.
State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.
a)
(5,3)
b)
(20,12)
c)
(-20,-12)
d)
(-5,-3)
76.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
77.
Dilate Point B by a scale factor of 1/2
a)
(1.5,-4)
b)
(-1.5,1)
c)
(-1,-1.5)
d)
(-2,-2)
78.
A dilation is which of the following: 
a)
only an enlargement
b)
only a reduction
c)
Either an enlargement or a reduction
d)
Neither an enlargement or a reduction
79.
What is the angle of rotation for this counterclockwise rotation about the origin?
a)
90°
b)
180°
c)
270°
d)
360°
80.
Name the series of transformations that maps ABC onto DEF
a)
reflect over x then translate left 6 up 1
b)
reflect over y then translate down 6 left 1
c)
translate right 6 down 1, then reflect over x
d)
rotate 90 clockwise then reflect over y
81.
What would be the coordinates of A' and B' if the image is reflected over the y-axis?
a)
A(1, 4), B(2, 1)
b)
A(-1, -4), B(-2, -1)
c)
A(1, -4), B(2, -1)
d)
A(-1, 4), B(-2, 1)
82.
Triangle ABC has vertices A(5,2).  Find the coordinates of ABC after a reflection over the x-axis.
a)
A’(5, -2)
b)
A’(-5, -2)
c)
A’(-5, -2)
83.
Mr. Triangle translated 4 units left and 1 unit up. What quadrant is he in now?
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV
84.
What translation does the pirate at D2 need to make to get to the treasure at E5?
a)
right 1, up 3
b)
right 3, up 1
c)
right 2, down 1
d)
right 2, up 2
85.
Triangle A is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?
a)
(x,y)→(y, -x) 
b)
(x,y)→(x,y)
c)
(x,y)→(-y,x)
d)
(x,y)→(-x,-y)
86.
A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?
a)
(5,3), (6,2), (1,-2)
b)
(6,0), (9,-3), (-6,-15)
c)
(2/3,0), (1,-1/3), (-2/3,-5/3)
d)
(-1,-3), (0,-4), (-5,-8)
87.
A transformation that “turns” a figure 90 degrees clockwise about the origin...
a)
(x,y) --> (-x, -y)
b)
(x,y) --> (y, -x)
c)
(x,y) --> (-y, x)
88.
How is Quadrilateral EFGH translated to E'F'G'H'?
a)
(x, y) --> (x, y - 6) 
b)
(x, y) --> (x + 1, y - 6)
c)
(x, y) --> (x- 3, y - 6)
d)
(x, y) --> (x - 3, y - 8)
89.
Algebraic Representation (Rule): (x,y) --> (x,-y)
a)
translates a figure down
b)
rotates a figure 90 degrees counterclockwise
c)
reflects a figure over the y axis
d)
reflects a figure over the x axis
90.

Which transformation preserves the shape and direction but NOT the size?

a)

translation

b)

rotation

c)

reflection

d)

dilation

91.

Which transformation preserves size, shape and direction?

a)

translation

b)

rotation

c)

reflection

d)

dilation

92.
What is the scale factor from ABCD to MNOP?
a)
2/3
b)
3/2
c)
2
d)
3
93.

The point A (8, 12) was dilated to become point A' (2, 3). What was the scale factor?

a)

½

b)

¼

c)

4

d)

2

94.

What is the scale factor of the dilation of ABC to XYZ?

a)

23\frac{2}{3}

b)

32\frac{3}{2}

c)

2

d)

3

95.

Point A is at (5, 8). Alice thinks that if you translate the point 6 units down and 2 units right then A' is at (-1, 10) because of (x - 6, y + 2). Identify her error.

a)

There is no error

b)

She should have done (x - 2, y + 6)

c)

She should have done (x + 2, y - 6)

d)

She should have done (y + 6, x - 2)

96.

Identify the transformation

A( 7, -4) --> A'( - 4, -7)

a)

translation

b)

rotation 90 degrees clockwise

c)

dilation

d)

rotation 270 degrees clockwise

e)

reflection across the x-axis

97.

Identify the transformation

A( 7, -4) --> A'( 3.5, -2)

a)

translation

b)

rotation 90 degrees clockwise

c)

dilation

d)

rotation 270 degrees clockwise

e)

reflection across the x-axis

98.

Identify the transformation

A( 7, -4) --> A'( 7, 4)

a)

translation

b)

rotation 90 degrees clockwise

c)

dilation

d)

rotation 270 degrees clockwise

e)

reflection across the x-axis

99.

Identify the transformation

A( 7, -4) --> A'( 9, 2)

a)

translation

b)

rotation 90 degrees clockwise

c)

dilation

d)

rotation 270 degrees clockwise

e)

reflection across the x-axis

100.

Identify the transformation

A( 7, -4) --> A'( 4, 7)

a)

translation

b)

rotation 90 degrees clockwise

c)

dilation

d)

rotation 270 degrees clockwise

e)

reflection across the x-axis

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