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Worksheets

Geometrical Transformations

Total questions: 119

Worksheet time: 3hrs 39mins

Name
Class
Date
1.
How many degrees was the figure rotated?
a)
90 degrees counterclockwise 
b)
180 degrees
c)
90 degrees clockwise
2.
If you were to rotate ABCD 180°  about the origin, what would the coordinate of A' be?
a)
(-5, 5)
b)
(-3, -5)
c)
(-5, 3)
d)
(-3, 3)
3.
The image A'B'C' is a rotation of ABC.
a)
True
b)
False
4.
Determine where x′ would be if you translated x three units to the left and two units down.
a)
(-4, 6)
b)
(-3, 1)
c)
(-4, 2)
d)
(-2, -4)
5.
How is trapezoid ABCD translated to trapezoid A'B'C'D'?
a)
Translated 5 units down and 5 units to the right
b)
Translated 5 units down and 1 to the right
c)
Translated 8 units down and 5 units to the right
d)
Translated 5 units down and 4 units to the right
6.
A transformation in which a graph or geometric figure is picked up and moved to another location without any change in size or direction.
a)
Translation
b)
Rotation
c)
Reflection
d)
Dilation
7.
If the dotted figure is the image, the original figure was reflected over the ...
a)
x-axis
b)
y-axis
8.
If the dotted figure is the image, the original figure was reflected over the ...
a)
x-axis
b)
y-axis
9.
You want to reflect a figure over the horizontal line shown. 
What directions would you give? 
Reflect over the line: ________
a)
x = -4
b)
y = -4
c)
x-axis
d)
None of these
10.
Which answer shows a reflection across the x-axis?
a)
d
b)
c
c)
b
d)
a
11.
Reflect over the x-axis.
Find K′.
a)
(4, 1))
b)
(-1, -4)
c)
(1, -4)
d)
(1, 4)
12.
Reflect (6, -3) over the line x-axis.
a)
(6, 3)
b)
(-6, -3)
c)
(-3, 6)
d)
(3, -6)
13.
Reflect the point (2, -4) over the y-axis.
a)
(-4, 2)
b)
(-2, 4)
c)
(-2, -4)
d)
(2, 4)
14.
What transformation is happening?
(x, y) ----> (x + 2, y - 3) 
a)
slide up 2, left 3
b)
slide right 2, up 3
c)
slide right 2, down 3
d)
slide left 3, right 2
15.
Point K (4, 2) is translated using this rule:
(x, y)----> (x + 3, y - 1) 
What are the coordinates of K'? 
a)
(6, 3)
b)
(7, 3) 
c)
(7, 1) 
d)
(5, 3) 
16.
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)
17.
A dilation is which of the following: 
a)
An enlargement
b)
A reduction
c)
Either an enlargement or a reduction
d)
Neither an enlargement or a reduction
18.
Identify the transformation from A to B.
a)
90o Clockwise Rotation
b)
180o Rotation
c)
270o  clockwise Rotation
d)
360o Rotation
19.
Identify the transformation from A to D.
a)
90o Clockwise Rotation
b)
180o Rotation
c)
270o  clockwise Rotation
d)
360o Rotation
20.
Identify the transformation from C to D.
a)
90o Counter Clockwise Rotation
b)
180o Rotation
c)
270o Counter clockwise Rotation
d)
360o Rotation
21.
Determine how to translate triangle ABC to triangle A'B'C'.
a)
(x-2, y+5)
b)
(x+2, y-9)
c)
(x-2, y+9)
d)
(x-9, y+2)
22.
The __________ is the ratio of a length of the image to the corresponding length on the original figure.
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
23.
Dilate Point A by a scale factor of 1/2
a)
(-4,-4)
b)
(-1,-4)
c)
(-1,-1)
d)
(-2,-2)
24.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
25.
Which of these transformations changes the size of the shape?
a)
Reflection
b)
Rotation
c)
Translation
d)
None of the Above
26.
What is the name of the transformed shape?
a)
image
b)
picture
c)
key
d)
prime
27.
How do you mark the transformed shape?
a)
tick
b)
comma
c)
prime
d)
period
28.

A dilation is

a)

Has a central point that stays fixed and everything else moves around that point

b)

a transformation that changes the size of a figure

c)

a transformation in which the preimage is flipped across a line

d)

a function that moves an object a certain distance. The object is not altered in any other way.

29.

A rotation

a)

Has a central point that stays fixed and everything else moves around that point

b)

a transformation that changes the size of a figure

c)

a transformation in which the preimage is flipped across a line

d)

a function that moves an object a certain distance. The object is not altered in any other way.

30.

A reflection

a)

Has a central point that stays fixed and everything else moves around that point

b)

a transformation that changes the size of a figure

c)

a transformation in which the preimage is flipped across a line

d)

a function that moves an object a certain distance. The object is not altered in any other way.

31.

A translation

a)

Has a central point that stays fixed and everything else moves around that point

b)

a transformation that changes the size of a figure

c)

a transformation in which the preimage is flipped across a line

d)

a function that moves an object a certain distance. The object is not altered in any other way.

32.

Which shows point (3, 6) rotated CLOCKWISE by 90 degrees?

a)

(6, -3)

b)

(-6, 3)

c)

(-3, -6)

d)

((3, 6)

33.

Which shows point (3, 6) rotated COUNTER-CLOCKWISE by 90 degrees?

a)

(6, -3)

b)

(-6, 3)

c)

(-3, -6)

d)

(3, 6)

34.

Which transformation is the only transformation that does NOT preserve size?

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

35.

True or False: all transformations except for dilations keep the figures congruent.

a)

TRUE

b)

FALSE

36.

What is the scale factor of this enlargement?

a)

1/2

b)

1/4

c)

2

d)

4

37.

What is the scale factor of this enlargement?

a)

1/2

b)

1/4

c)

2

d)

4

38.

What is the scale factor of this reduction?

a)

1/2

b)

1/4

c)

2

d)

4

39.

What is the scale factor of this reduction?

a)

1/2

b)

1/4

c)

2

d)

4

40.
When you translate, (x,y+6) will move _____.
a)
6 units right
b)
6 units left
c)
6 units up
d)
6 units down
41.

A triangle is dilated by a scale factor of 4 and then translated left 2 units and up 3 units. Which statement is true about the image and the pre-image?

a)

The pre-image and image are congruent and similar to one another.

b)

The pre-image and image are neither congruent nor similar to one another.

c)

The pre-image and image are congruent, but not similar to one another.

d)

The pre-image and image are similar, but not congruent to one another.

42.

Trapezoid PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'. Which statement is true?

a)

The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

b)

Trapezoid PQRS is not congruent to trapezoid P'Q'R'S'.

c)

The area of trapezoid PQRS is less than the area of trapezoid P'Q'R'S'.

d)

The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid P'Q'R'S'.

43.

When a figure is dilated, its image is ?????.

a)

Congruent

b)

Similar

c)

Not Here

44.
Point (6,7) is translated according to the algebraic representation (rule) (x,y) --> (x-2,y+3).  Where is the point located now?
a)
(8,10)
b)
(4,10)
c)
(4,4)
d)
(8,4)
45.
When you dilate, you ______ x and y by a number.
a)
Multiply
b)
Add
c)
Subtract
d)
Divide
46.
Congruent geometric figures have the:
a)
Same size
b)
Sides Equal
c)
Same Size and Same Shape
d)
Angles Equal
47.
Which of the following describes the sequence of transformations shown?
a)
Reflect across the x-axis and then rotate -90 degrees around the origin
b)
Rotate -90 degrees 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 about the origin.
48.
Reflect (6, -3) over the line x-axis.
a)
(6, 3)
b)
(-6, -3)
c)
(-3, 6)
d)
(3, -6)
49.
Reflect Point C over the y-axis:
a)
(-3, 2)
b)
(3,2)
c)
(-2,3)
d)
(3,0)
50.
The original figure prior to a transformation.
a)
Pre-image
b)
Image
51.
What transformation is happening?
(x, y) ----> (x + 2, y - 3) 
a)
slide up 2, left 3
b)
slide right 2, up 3
c)
slide right 2, down 3
d)
slide left 3, right 2
52.
Write the rule for this translation:
Slide 3 up and 2 right
a)
(x, y)---->(x + 3, y + 2)
b)
(x, y)-----> (x+2, y + 3)
c)
(x, y)----> (x - 2, y + 3)
53.
Point M (-3, 5) is translated using this rule. 
(x, y) ----> (x - 1, y) 
What are the coordinates of M'?
a)
(-4, 5)
b)
(-2, 5)
c)
(-4, 4)
d)
None of these
54.
Will the following transformations result in a congruent or similar figure?
1. Rotation 90 degrees, clockwise, center at point C
2. Dilation with scale factor of 1/2, center at (-1, -2)
a)
Congruent
b)
Similar
55.
Will the following transformations result in a congruent or similar figure?
1. Reflection over the line x = -3
2. Rotation of 180 degrees, center at (4, 5)
a)
Congruent
b)
Similar
56.
a)
Reflections
b)
Translations
c)
Reflections and Rotations
d)
Translations and Rotations
57.
What is the sequence of transformations for the image given? 
a)
Reflect over the x-axis, translate (x+8,y)
b)
Reflect over the x-axis then translate (x+6, y)
c)
Reflect over the y-axis then (x+1, y+1)
d)
Translate down 4 (y-4) and to the right 5 (x+5)
58.

Which of the following would represent a dilation with a scale factor of 2.5?

a)

enlargement

b)

reduction

59.

Which of the following would represent a dilation with a scale factor of 0.5?

a)

enlargement

b)

reduction

60.

Which of the following would represent a translation of 6 units to the left and 4 units up?

a)

(x,y) --> (x - 6, y + 4)

b)

(x,y) --> (x + 6, y - 4)

c)

(x,y) --> (6x, 4y)

d)

(x,y) --> (x + 4, y - 6)

e)

(x,y) --> (y + 4, x - 6)

61.

Which of the following would represent a translation of 8 units down and 2 units to the right?

a)

(x,y) --> (x + 2, y - 8)

b)

(x,y) --> (x - 2, y + 8)

c)

(x,y) --> (2x, 8y)

d)

(x,y) --> (x - 8, y + 2)

e)

(x,y) --> (y - 8, x + 2)

62.

Which of the following would represent a dilation with a scale factor of 2.5?

a)

(x,y) --> (2.5x, 2.5y)

b)

(x,y) --> (2.5y, 2.5x)

c)

(x,y) --> (x + 2.5, y + 2.5)

d)

(x,y) --> (-2.5x, -2.5y)

63.

Which of the following would represent a dilation with a scale factor of 0.5?

a)

(x,y) --> (0.5x, 0.5y)

b)

(x,y) --> (0.5y, 0.5x)

c)

(x,y) --> (x + 0.5, y + 0.5)

d)

(x,y) --> (-0.5x, -0.5y)

64.
Translation are always _______
a)
Congruent
b)
Bigger
c)
Smaller
d)
Rotated
65.
Translation are always _______
a)
Congruent
b)
Bigger
c)
Smaller
d)
Rotated
66.
A dilation produces a congruent figure
a)
True
b)
False
c)
D
67.
A dilation produces a similar figure
a)
True
b)
False
68.

When you translate, you ______ a number to x and y.

a)

Add or subtract

b)

Multiply or divide

c)

Add or multiply

d)

Subtract or divide

69.
Write a rule for the translation.
a)
 (x -1, y  + 2)
b)
 (x -2, y  + 1)
c)
 (x +2, y  - 1)
d)
(x +1, y  -  2)
70.

What is the rule for the dilation pictured below?

a)

(x, y) → (½x, ½y)

b)

(x, y) → (x + 2, y + 2)

c)

(x, y) → (2x, 2y)

d)

(x, y) → (2x, 3y)

71.
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
72.
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)
73.
The result of a transformation.
a)
Pre-image
b)
Image
74.
How many degrees was the figure rotated?
a)
90 degrees counterclockwise 
b)
180 degrees
c)
90 degrees clockwise
75.
If you were to rotate ABCD 180° about the origin, what would the coordinates of B' be?
a)
(0, 0)
b)
(-6, -5)
c)
(-1, 3)
d)
(-6, 2)
76.
∆QRS contains the points: Q(4, 2) R(5, 1) S(3,7). If the triangle is reflected across the y-axis, what will S' be?
a)
S'(3, 7)
b)
S'(-3, 7)
c)
S'(-3, -7)
d)
S'(3, 7)
77.
What is the sequence of transformations for the image given? 
a)
Reflect over the x-axis, translate (x+8,y)
b)
Reflect over the x-axis then translate (x+6, y)
c)
Reflect over the y-axis then (x+1, y+1)
d)
Translate down 4 (y-4) and to the right 5 (x+5)
78.
What is the sequence of transformations for the image given? 
a)
Reflect over the x-axis, translate (x+8,y)
b)
Reflect over the x-axis then translate (x+6, y)
c)
Reflect over the y-axis then (x+1, y+1)
d)
Translate down 4 (y-4) and to the right 5 (x+5)
79.
A dilation with a scale factor of 2 is a reduction. 
a)
True
b)
False
80.
C(-6, 2) and B(-1, -1)
Rotate 90 degrees counterclockwise.
a)
C' (-6, 2), B' (-1, -1)
b)
C' (6, 2), B' (1, -1)
c)
C' (2, -6), B' (-1, -1)
d)
C' (-2, -6), B' (1, -1)
81.
A(-2, 2) and B(3, 2)
Rotate 180 degrees 
a)
A' (-2, 2), B' (3, 2)
b)
A' (-2, -2), B' (-3, -2)
c)
A' (2, -2), B' (-3, -2)
d)
A' (2, -2), B' (2, 3)
82.
A(-2, 2) and B(3, 2) 
Dilate k = 2 
a)
A' (-2, 2), B' (3, 2)
b)
A' (-4, 4), B' (6, 4)
c)
A' (2, -2), B' (-3, -2)
d)
A' (2, -2), B' (2, 3)
83.
An office supply store sells index cards in two different sizes. The large size is an enlargement of the small size. Both sizes are shown. Find the scale factor of the enlargement.
a)
2
b)
3
c)
4
d)
5
84.

Rectangle EFGH has the following coordinates:

E ( -3, 6)

F ( 3, 6)

G ( 3, -6)

H ( -3, -6)


Dilate the rectangle by a scale factor of 1/3. What are the coordinates of G'?

a)

(1, -3)

b)

(1, -2)

c)

(-1, 2)

d)

(-3, 6)

85.

What type(s) of transformations result in congruent figures or isometries?

SELECT ALL THAT APPLY

a)

Translation

b)

Dilation

c)

Rotation

d)

Reflection

86.
A transformation that “turns” a figure about a fixed point at a given angle and a given direction.
a)
rotation
b)
translation
c)
reflection
d)
dilation
87.

Moving a point or a shape in cardinal directions (left, right, up, or down) is called a...

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

88.

Translations, reflections and rotations are all known as ________________________.

a)

Geometry

b)

Transformations

c)

Congruent

d)

Rigid motion

89.

Translations, rotations, and reflections are always _______

a)

Congruent

b)

Bigger

c)

Smaller

d)

Rotated

90.
When you translate, (x,y+6) will move _____.
a)
6 units right
b)
6 units left
c)
6 units up
d)
6 units down
91.
When you reflect a shape, you ______ over an axis or line.
a)
Flip
b)
Rotate
c)
Slide
d)
Expand
92.
Which rule would result in a translation of 2 units left and 3 units up?
a)
(x, y) → (2x, 3y)
b)
(x, y) → (x - 2, y + 3)
c)
(x, y) → (-x, -y)
d)
(x, y) → (x + 2, y - 3)
93.
Point (-5,2) is reflected over the y axis.  Where is the new point located?
a)
(5,2)
b)
(-5,-2)
c)
(-5,2)
d)
(5,-2)
94.

The __________ is the ratio of a length of the image to the corresponding length on the original figure. (new / old)

a)

reduction

b)

enlargement

c)

scale factor

d)

center of dilation

95.

A dilation with k = 0.75 is which?

a)

An enlargement

b)

A reduction

c)

Either an enlargement or a reduction

d)

Neither an enlargement or a reduction

96.
Does a translation left/right go with x or y?
a)
x
b)
y
c)
z
d)
q
97.

Does a translation up/down go with x or y?

a)

x

b)

y

c)

z

d)

q

98.

Dilations have which operation?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

99.
When a dilation has a scale factor greater than one, the dilation is an enlargement.
a)
True
b)
False
100.
When the scale factor of a dilation is less than one, the dilation is a reduction.
a)
True
b)
False
101.
Does the image show a dilation?
a)
Yes
b)
No
102.
In a dilation what mathematical operation is used with the scale factor?
a)
addition 
b)
subtraction 
c)
multiplication 
d)
division 
103.

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

104.

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

a)

B' (2 , 4.5)

b)

B' (-8 ,-18)

c)

B' (8 ,18)

d)

B' (9 ,4)

105.

When A(3, 6) is under a dilation of 2 what are the coordinates of A'?

a)

(3, 6)

b)

(1.5, 3)

c)

(6, 12)

d)

(12, 6)

106.

A dilation produces a congruent figure

a)

True

b)

False

107.
The __________ is the ratio of a length of the new figure to the corresponding length on the original figure.
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
108.

State the coordinate of the image of the given point G (-10,-6) under a dilation with center at the origin with the given scale factor of 1/2.

a)

G' (5,3)

b)

G' (20,12)

c)

G' (-20,-12)

d)

G' (-5,-3)

109.
Similar figures have the same ______ but different ______. 
a)
measure; shapes
b)
sizes; shapes
c)
value; measures
d)
shape; sizes
110.

If your SF = 0.8, what type of dilation is it?

a)

Reduction

b)

Enlargement

111.

If your SF = 2.5, what type of dilation is it?

a)

Reduction

b)

Enlargement

112.

If your SF = 6/5, what type of dilation is it?

a)

Reduction

b)

Enlargement

113.
Tell whether each transformation is a dilation. Explain.
a)
No, scale factor isn't the same.
b)
Yes, scale factor is the same
114.
Tell whether the transformation is a dilation. Explain.
a)
No, scale factor isn't the same.
b)
Yes, scale factor is the same.
115.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
116.
Triangle D is rotated 360° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?
a)
A
b)
B
c)
C
d)
D
117.
Triangle B is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?
a)
A
b)
B
c)
C
d)
D
118.
Triangle D is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?
a)
A
b)
B
c)
C
d)
D
119.
Triangle C is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?
a)
A
b)
B
c)
C
d)
D

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