Free Printable Transformations

1.

The original figure prior to a transformation.

a)

Pre-image

b)

Image

2.

Reflect the point (2, -4) over the y-axis.

a)

(-4, 2)

b)

(-2, 4)

c)

(-2, -4)

d)

(2, 4)

3.

Reflect (6, -3) over the line x-axis.

a)

(6, 3)

b)

(-6, -3)

c)

(-3, 6)

d)

(3, -6)

4.

When you rotate 180 degrees the ( x , y ) becomes ?

a)

( y , x )

b)

( -y , x )

c)

( -x , y )

d)

( -x , -y )

5.

When you rotate 90 degrees clockwise ( x , y ) becomes ?

a)

( -x , -y )

b)

( y , -x )

c)

( y , x )

d)

( -y , -x )

6.

Triangle A is rotated 90° 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

7.

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)

8.

If the rectangle were rotated 90º clockwise about the origin, what would be the coordinates of Z'?

a)

(2, -2)

b)

(-2, -3)

c)

(2, 2)

d)

(-3, -2)

9.

If the triangle is reflected across the y-axis, the coordinates of the new triangle will be (5, 0), (2, 3), and ___.

a)

(0, 5)

b)

(4, 3)

c)

(3, 5)

d)

(2, 3)

10.

If the rectangle were rotated 90º counterclockwise about the origin, what would be the location of K'?

a)

(1, -6)

b)

(-1, 6)

c)

(6, -1)

d)

(-6, -1)

11.

If (4,-2) → (4,-2) represents a counterclockwise rotation of the point on a coordinate plane, how many degrees is the rotation?

a)

90

b)

180

c)

270

d)

360

12.

Which transformation(s), no matter which one you do, will the resulting image be congruent? (select all that apply)

a)

translation

b)

reflection

c)

rotation

d)

dilation

13.

The result of a transformation.

a)

Pre-image

b)

Image

14.

What is the angle of rotation for this counterclockwise rotation about the origin?

a)

90°

b)

180°

c)

270°

d)

360°

15.

Which algebraic rule will produce a translation that is 5 units to the right?

a)

(x, y) --> ( x , y + 5)

b)

(x, y) --> ( x-5 , y + 5)

c)

(x, y) --> ( x-2 , y + 5)

d)

(x, y) --> ( x+5 , y)

16.

What type of transformation is shown?

a)

Rotation

b)

Translation

c)

Reflection

17.

What type of transformation is shown?

a)

Translation

b)

Reflection

c)

Rotation

18.

If (3,2)→(-3,-2) represents a counterclockwise rotation of the point on a coordinate plane, how many degrees is the rotation?

a)

90

b)

180

c)

270

d)

360

19.

What is the algebraic representation for the transformation shown?

a)

(x, y) ---> (x - 8, y + 3)

b)

(x, y) ---> (x - 4, y + 9)

c)

(x, y) ---> (x + 8, y - 3)

d)

(x, y) ---> (x + 4, y - 9)

20.

What transformation is the following rule for?

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

a)

Reflect over the x axis

b)

Reflect over the y-axis

c)

Rotate 90 degrees clockwise

d)

Rotate 270 degrees clockwise

21.

Translations, rotations, and reflections are three different types of what?

a)

Transformations

b)

Geometry

c)

Vectors

d)

Shapes

22.

When you translate, (x-4 ,y) will move _____.

a)

4 units right

b)

4 units left

c)

4 units up

d)

4 units down

23.

Identify the transformation from ABC to A'B'C'.

a)

90^o clockwise rotation

b)

90^o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

24.

What is this picture an example of?

a)

Reflection

b)

Translation

c)

Rotation

d)

Dilation

25.

What is the ordered pair for C' if reflected over the y-axis?

a)

(-3, 2)

b)

(3, 2)

c)

(-2, 3)

d)

(3, 0)

26.

Determine how to translate triangle ABC to triangle A'B'C'.

a)

right 2, down 5

b)

right 2, down 9

c)

left 2, up 9

d)

left 2, down 9

27.

Which answer shows a reflection across the y-axis?

a)

a

b)

b

c)

c

d)

d

28.

A slide is also called a _________.

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

29.

A turn is also called a ___________.

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

30.

Describe the Transformation

a)

Translation

b)

Rotation

c)

Reflection

31.

Zach and Naomi are studying geometric transformations. Zach is able to move the triangle $A$ to $A'$ using the following sequence of basic transformations:

1. Reflection across the x-axis.
2. Reflection across the y-axis.
3. Translation two units to the right.
Naomi claims that the same three transformations, done in any order will always produce the same result. Zach disagrees. Who is correct?

a)

Zach

b)

Naomi

c)

Both are correct

d)

Both are incorrect

32.

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.

33.

Which pair of cards show a shape and its image after a rotation?

a)

1 and 4

b)

2 and 6

c)

3 and 5

34.

Which pair of cards shows a shape and its image after a reflection?

a)

1 and 4

b)

2 and 6

c)

3 and 5

35.

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

36.

A type of transformation where a figure is “flipped” over a line.

a)

rotation

b)

translation

c)

dilation

d)

reflection

37.

A slide is also called a _________.

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

38.

a)

FG

b)

HI

c)

BC

d)

DE

39.

Which of the following is NOT a rigid transformation?

a)

b)

c)

d)

40.

Which figure is the IMAGE?

a)

ABC

b)

A'B'C'

c)

Not enough information

41.

Describe the reflection.

a)

Reflect over the x-axis

b)

Reflect over the y-axis

c)

Reflect 180 degrees

d)

Reflect over the origin

42.

Which of the following has been PRESERVED?

Select all that apply.

a)

Size

b)

Shape

c)

Orientation

d)

None of these

43.

Translations, reflections and rotations are all known as ________________________.

a)

Geometry

b)

Rigid Transformations

c)

Congruent

d)

Non- Rigid Transformations

44.

If P is the pre-image and Q the image, select the correct segment that translates P to Q.

a)

b)

c)

d)

45.

A rigid motion ...

a)

preserves size and location

b)

preserves shape and location

c)

preserves size and shape

d)

makes the figure larger

46.

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

47.

What transformation is happening?

T_{(x + 2, y - 3)}

a)

translate up 2, left 3

b)

translate right 2, up 3

c)

translate right 2, down 3

d)

translate left 3, right 2

48.

Rotate the point (7,8) around the origin 90 counter clockwise degrees. State the image of the point.

a)

(-7,-8)

b)

(8,-7)

c)

(-8,7)

d)

(8,7)

49.

Reflect the point (2, -4) over y = x.

a)

(-4, 2)

b)

(-2, 4)

c)

(-2, -4)

d)

(2, 4)

50.

Reflect the point D (-9, -12) over the line y = -x.

a)

(12, 9)

b)

(-12, -9)

c)

(-12, 9)

d)

(12, -9)

51.

True or false: When a point is reflected across a line of reflection, the image is the same distance from the line as the preimage.

a)

true

b)

false

52.

Under what composition of transformations does triangle ABC map onto triangle A''B''C''

a)

Reflection over x-axis, then Rotation of 90 Degrees

b)

Rotation of -90 Degrees, then Reflection over y-axis

c)

Reflection over y-axis, then Rotation of -90 Degrees

d)

Rotation of 90 Degrees, then Reflection over x-axis

53.

What is the transformation from Triangle ABC to Triangle A''B''C''?

a)

Reflection x-axis, then rotation of 180 Degrees

b)

Reflection over y-axis, then rotation of 90 Degrees

c)

Rotation of 90 Degrees, then reflection over x-axis

d)

Rotation of 180 Degrees, then reflection over y-axis

54.

Which way do you rotate if you turn to the right?

a)

clockwise

b)

counterclockwise

c)

flip-flop

d)

upside down

55.

What is the proper term for rotating to the left?

a)

clockwise

b)

spin

c)

counter-clockwise

d)

time

56.

Reflection across the x-axis rule is.....

a)

(x, -y)

b)

(-x, y)

57.

Reflection across the y-axis rule is....

a)

(x, -y)

b)

(-x, y)

58.

Reflection across y = x rule is....

a)

(-y, -x)

b)

(y, x)

59.

Reflection across y = -x rule is ....

a)

(y, x)

b)

(-y, -x)

60.

Rotation of 90 degrees clockwise and 270 degree counter-clockwise rule is....

a)

(y, -x)

b)

(-y, x)

61.

Rotation of 90 degrees counter-clockwise and 270 degree clockwise rule is ...

a)

(y, - x)

b)

(-y, x)

62.

Rotation of 180 degrees both clockwise or counter-clockwise rule is....

a)

(y, x)

b)

(-x, -y)

63.

Reflect the figure over the line y=x. What are the coordinates of C' ?

a)

(4, -2)

b)

(-4, 2)

c)

(2, 4)

d)

(4, 2)

64.

Which of the following can be described as a single translation, rotation or reflection instead of a composition of rigid motions? (Select all that apply)

a)

$R_{q\ }\circ\ R_p$

b)

$T_{\left(c,\ d\right)}\ \circ\ R_{\ x\ axis}$

c)

$T_{\left(d,\ e\right)}\ \circ\ r_{\left(45\degree,\ P\right)}$

d)

$T_{\left(f,\ g\right)}\ \circ\ T_{\left(c,\ d\right)}$

65.

Which composition of rigid motions the same as $r_{\left(180\degree,\ O\right)}\ \left(\Delta ABC\right)$ ?

a)

$r_{\left(-90\degree,\ O\right)}\left(\Delta ABC\right)$

b)

$\left(R_{x-axis}\ \circ\ R_{y-axis}\right)\ \left(\Delta ABC\right)$

c)

$T_{\left(0,5\right)}\ \circ\ T_{\left(-5,\ 0\right)}\ \left(\Delta ABC\right)$

d)

$r_{\left(360\degree,O\right)}\left(\Delta ABC\right)$

66.

Line segment CD is rotated $110\degree$ counterclockwise around F and then $35\degree$ clockwise around F. Which of the following is the composition of transformations for C?

a)

$r_{\left(35\degree,\ F\right)}\ \circ\ r_{\left(-110\degree,\ F\right)}\left(C\right)$

b)

$r_{\left(110\degree,\ F\right)}\ \circ\ r_{\left(-35\degree,\ F\right)}\left(C\right)$

c)

$r_{\left(-110\degree,\ F\right)}\ \circ\ r_{\left(35\degree,\ F\right)}\left(C\right)$

d)

$r_{\left(-35\degree,\ F\right)}\ \circ\ r_{\left(110\degree,\ F\right)}\left(C\right)$

67.

You notice the single transformation $r_{\left(80\degree,\ T\right)}\left(C\right)\ =\ D$ and the composition $R_{\overline{TE}}\ \circ\ R_{\overline{TF}}\ \left(C\right)\ =\ D$ . What is the $m\angle FTE$ ?

a)

Not enough information

b)

$80\degree$

c)

$40\degree$

d)

$160\degree$

68.

Which type of rigid transformation is the equivalent of two reflections over two horizontal lines?

a)

rotation

b)

reflection

c)

dilation

d)

translation

69.

Which type of rigid transformation is the equivalent of two reflections over two parallel lines?

a)

translation

b)

reflection

c)

double rotation

d)

rotation

70.

Which type of rigid transformation is the equivalent of two reflections over intersecting lines?

a)

translation

b)

reflection

c)

double rotation

d)

rotation

71.

Which type of rigid transformation is the equivalent of two reflections -- over the x-axis then the y-axis?

a)

translation

b)

reflection

c)

double rotation

d)

rotation

72.

Select all that apply. The equation y = 0 is :

a)

the x-axis

b)

a horizontal line

c)

a vertical line

d)

the y-axis

73.

A double reflection over two parallel line results in a ____________.

a)

Reflection

b)

Translation

c)

Rotation

74.

A double reflection over two intersecting lines results in a _______

a)

rotation

b)

reflection

c)

translation

75.

A __________ describes a transformation in which a figure, point, line, or segment is "moved" or "slid" across a specific x and y direction on a coordinate plane.

a)

Reflection

b)

Rotation

c)

Translation

d)

Dilation

76.

A __________ describes a transformation in which a figure, point, line, or segment is "mirrored" across a specific line or point on a coordinate plane.

a)

Reflection

b)

Rotation

c)

Translation

d)

Dilation

77.

A __________ describes a transformation in which a figure, point, line, or segment is "turned" by a specific degree in either a clockwise or counter-clockwise direction and in respect to a fixed point on a coordinate plane.

a)

Reflection

b)

Rotation

c)

Translation

d)

Dilation

78.

The pre-image of a figure is what the figure looks like before it is transformed.

a)

True

b)

False

79.

The image of a figure is what the figure looks like after it is transformed.

a)

True

b)

False

80.

The order for a composition of transformations (combinations of two or more transformations) are read from right to left?

a)

True

b)

False

81.

What does it mean for a transformation to be a rigid motion?

(select multiple answers if they correctly apply.)

a)

The transformation preserves:

distance

b)

The transformation preserves:

perpendicularity

c)

The transformation preserves:

size

d)

The transformation preserves:

angle measures

82.

If a figure is reflected twice, across two intersecting lines, the angle of rotation is ________ the angle formed by the intersecting lines

a)

half

b)

equal to

c)

twice

83.

If a figure is reflected twice, across two parallel lines, the total translated distance is _________ the distance between the parallel lines

a)

half

b)

equal to

c)

twice

Transformations

Total questions: 83

Worksheet time: 7hrs 55mins

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