wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Dilations and Multiple Transformations

Total questions: 50

Worksheet time: 2hrs 54mins

Name
Class
Date
1.
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)
2.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
3.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
4.
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)
5.

TRUE or FALSE:


A dilation produces an image that is similar to the pre-image.

a)

True

b)

False

6.

TRUE OR FALSE:


When a dilation has a scale factor greater than one, the dilation is an enlargement.

a)

True

b)

False

7.
How do you write the algebraic notation when the scale factor is 3?
a)
(x, y) goes to (1/3x, 1/3y)
b)
(x, y) goes to (-3x, -3y)
c)
(x, y) goes to (x + 3, y + 3)
d)
(x, y) goes to (3x, 3y)
8.
Identify the transformation from ABC to A'B'C'.
a)
Reflection across the x-axis
b)
Reflection across the y-axis
c)
90o clockwise rotation
d)
90o counterclockwise rotation
9.

TRUE OR FALSE:


The image A'B'C' is a rotation of ABC.

a)

True

b)

False

10.

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.

11.
Which rule shows the transformation?
a)
(x, y) ----> (0.5x, 0.5y)
b)
(x, y) ----> ( 2 + x, 2 + y)
c)
(x, y) -----> (2x, 2y)
d)
(x, y) -----> (3x, 3y)
12.
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
13.

Pre-Image: (2, 6)


Translate up 3, left 1 and rotate 180°


Image:

a)

(-1,-9)

b)

(1, -9)

c)

(5,5)

d)

(-5,5)

14.

Pre-Image: (-3, -1)


Reflect across the line y = x and translate down 1


Image:

a)

(-1, -4)

b)

(-1, -2)

c)

(3, 0)

d)

(-2, -3)

15.

Choose the correct transformations

a)

rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis

b)

right 1, down 4, and then reflection over the y-axis

c)

right 6, and then reflection over the x-axis

d)

reflection over the line y=x, and then translate up 4, right 2

16.

Identify the transformations:

a)

rotation

b)

reflection

c)

translation

d)

dilation

17.

Point A is rotated 180 degrees and then flipped over the y-axis. What is A" if A is (2,7)

a)

(2,7)

b)

(-2, -7)

c)

(-2, 7)

d)

(2, -7)

18.

Find Q''' if Q(-3, 1) is:


reflected over the x-axis

rotated 90 degrees ccw

translated right 3 and up 4

a)

(-3, 1)

b)

(4, 1)

c)

(4, -1)

d)

(-3,-1)

19.

Triangle ABC is rotated 90 degrees ccw ,and then translated up 4 and left 5. What is point A if point A''' is (1,2)?

a)

(2, -4)

b)

(2,6)

c)

(4, -2)

d)

(-2 -6)

20.

Given the triangle  A(2,3) B(5,3) C(5,0)A\left(2,3\right)\ B\left(5,3\right)\ C\left(5,0\right)  under a dilation with a scale factor of  43\frac{4}{3}  . What are the coordinated for the image?

a)

 A(83,4) B(203,4)C(203,0)A\left(\frac{8}{3},4\right)\ B\left(\frac{20}{3},4\right)C\left(\frac{20}{3},0\right)  

b)

 A(2.6,4)B(4,6.7) C(4,0)A\left(2.6,4\right)B\left(4,6.7\right)\ C\left(4,0\right)  

c)

 A(23,1) B(53,1) C(53,0)A\left(\frac{2}{3},1\right)\ B\left(\frac{5}{3},1\right)\ C\left(\frac{5}{3},0\right)  

21.
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)
22.
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 k = 2.
a)
(2,4.5)
b)
(-8,-18)
c)
(8,18)
d)
(9,4)
23.

A figure is dilated so that point C(2, 9) becomes C'(8, 36). what is the rule for this transformation?

a)

(x, y) --> (1/4x, 1/4y)

b)

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

c)

(x, y) --> (x + 6, y + 27)

d)

Not here

e)

(x, y) --> (x - 6, y - 27)

24.

A figure is dilated so that point C(8, 36) becomes C'(2, 9). what is the rule for this transformation?

a)

(x, y) --> (1/4x, 1/4y)

b)

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

c)

(x, y) --> (x - 6, y - 27)

d)

Not here

e)

(x, y) --> (x + 6, y + 27)

25.

What is the rule for this transformation?

a)

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

b)

(x, y) --> (1/2x, 1/2y)

c)

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

d)

Not here

26.

Which transformation(s) preserve congruency?

(Choose all that apply)

a)

rotations

b)

reflections

c)

translations

d)

dilations

27.
Dilate Point B by a scale factor of 3:
a)
(12,0)
b)
(12,12)
c)
(4,3)
d)
(0,12)
28.

Choose the correct scale factor:

a)

2.5

b)

1.5

c)

3.5

d)

4

29.
Triangle ABC has vertices A (-2, 2), B (2, 4) and C (3, -1).  What are the coordinates of A' after a dilation by a scale factor of 2.5?
a)
(-5, 5)
b)
(5, -5)
c)
(5, 10)
d)
(7.5, -2.5)
30.
Rectangle ABCD is dilated so that A' is located at (3, 6).  What could be the dilation rule?
a)
(2x, 3y)
b)
(2/3 x, 2/3 y)
c)
(3/2 x, 3/2 y)
d)
(x + 2, y + 3)
31.
Rectangle ABCD is dilated so that the coordinates of C' are (2, -1).  What could be the dilation rule?
a)
(-2x, +1y)
b)
(1/2 x, 1/2 y)
c)
(2x, 2y)
d)
(x - 2, y - 1)
32.
Quadrilateral RSTV is dilated so that the coordinates of S' are (3, 9).  What was the scale factor of the dilation?
a)
0.6
b)
(1, 3)
c)
3/2
d)
3
33.
Triangle ABC is dilated so that the coordinates of C' are (2, -1).  What was the scale factor of the dilation?
a)
3
b)
2
c)
1/2
d)
1/3
34.

Which algebraic expression could be the rule for a reduction?

a)

(x, y)→(2x, 2y)

b)

(x, y)→(5/2x, 5/2y)

c)

(x, y) →(0.5x, 0.5y)

d)

(x, y)→(5x, 5y)

e)

(x, y)→(0.8x, 0.8y)

35.

Polygon ABCDE will be dilated by a scale factor of 2. Select the true statement(s).

a)

The corresponding angles of the two polygons will be equal.

b)

The dilation will be an enlargement.

c)

The pre-image and the image will be congruent.

d)

Polygon A'B'C'D'E' will be proportional to polygon ABCDE.

36.
Enlargement or reduction?  Find the scale factor!
a)
It's an enlargement; the scale factor is 3.
b)
It's a reduction; the scale factor is 1/3.
c)
It's a reduction; the scale factor is 1/2.
d)
It's an enlargement; the scale factor is 2. 
37.
Which could be the rule used to dilate ABC to A'B'C'?
a)
(5x, 5y)
b)
(3x, 3y)
c)
(1/3 x, 1/3 y)
d)
(2x, 2y)
38.

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

39.

If the red triangle is rotated 180 degrees, then reflected over y=2 what is the final image?

a)

Green Triangle

b)

Blue Triangle

c)

Orange Triangle

d)

Red Triangle

40.

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

41.

A reflection over the x-axis followed by a reflection over the y-axis is the same as a ...

a)

Rotation of 180 Degrees

b)

Rotation of 90 Degrees ccw

c)

Reflection over the x-axis

d)

Reflection over the y-axis

e)

Rotation of 90 Degrees cw

42.

Describe the transformations that map ABC onto A"B"C"

a)

translate 5 up and 1 left, then reflect over y-axis

b)

translate 5 down and 1 left, then reflect over y-axis

c)

reflect over y = x, then translate left 8

d)

reflect over x-axis, then rotate 90 degrees clockwise

43.

Name the series of transformations that maps ABC (the pre-image) onto DEF (the image).


The dotted triangle is the transformation between ABC and DEF.

a)

reflect over x-axis, then translate left 6 up 1

b)

reflect over y-axis, then translate down 6 left 1

c)

translate right 6 down 1, then reflect over x-axis

d)

rotate 90 clockwise, then reflect over y-axis

44.

Segment AB is the pre-image. Which segments could be the image if translations, rotations, or reflections were applied?


Select all that apply.

a)

CD

b)

GH

c)

JK

d)

LM

e)

NP

45.

Find the image of A( -3, 5) after:


1. (x,y) --> (x , y - 4)

2. reflect across the y-axis

a)

(3,1)

b)

(3, -1)

c)

(-1, 5)

d)

(-1, 3)

46.

What is the ordered pair for the final location of P( -7, 3) after this series of transformations?  (x,y)→(x, y+3)\left(x,y\right)\rightarrow\left(x,\ y+3\right)  then rotated  90°90\degree  clockwise about the origin.

a)

 P′(−7, 6)P'\left(-7,\ 6\right)  

b)

 P′(−7, −6)P'\left(-7,\ -6\right)  

c)

 P′(6, −7)P'\left(6,\ -7\right)  

d)

 P′(6, 7)P'\left(6,\ 7\right)  

47.

Which sequence of transformations is used to transform the original image to the final image?


Pre-Image: ABCD

Image: A" B" C"D"

a)

Reflect over the x-axis, then rotate clockwise 90 around the origin.

b)

Rotate counterclockwise 90 around the origin, then translate 8 units left.

c)

Reflect over the y-axis, then rotate counterclockwise 90 around the origin.

d)

Rotate clockwise 90 around the origin, then translate 8 units left.

48.

Quadrilateral QRST is rotated 360 counterclockwise around a center at one of its vertices. Which statements must be true? Select all that apply.

a)

Q'R'S'T' appears as a translation of QRST .

b)

Q'R'S'T' appears as a reflection of QRST .

c)

The coordinate x- and y-values of Q'R'S'T' are the same as QRST coordinate x- and y-values

d)

Image Q'R'S'T' is mapped exactly on top of QRST .

e)

The coordinate x- and y-values of Q'R'S'T' are the reverse of QRST coordinate x- and y-values

49.

Which transformations could be used to transform from the original image to the final image?

a)

Translate 7 units down, then reflect across the y-axis.

b)

Translate 8 units right, then rotate 180.

c)

Rotate 90 counterclockwise, then translate 8 units right.

d)

Rotate 180 around the origin, then translate 7 units up.

50.

What are the series of rigid motions that would map ∆ABC onto ∆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

Similar Resources on Wayground

SOH CAH TOA

45 questions

SOH CAH TOA

quiz

Worksheet

•

11th Grade

MATEMATIKA KELAS 5

50 questions

MATEMATIKA KELAS 5

quiz

Worksheet

•

11th Grade

VARIABLES, TABLAS Y GRAFICAS ESTADÍSTICAS

51 questions

VARIABLES, TABLAS Y GRAFICAS ESTADÍSTICAS

quiz

Worksheet

•

9th Grade

2R Form 2 Chapter 13

50 questions

2R Form 2 Chapter 13

quiz

Worksheet

•

8th Grade

Limit

50 questions

Limit

quiz

Worksheet

•

10th - 12th Grade

MATH9 - 4th Summative Test Reviewer

50 questions

MATH9 - 4th Summative Test Reviewer

quiz

Worksheet

•

9th Grade

Asesmen Formatif Kls-9 Topik Penjabaran & Pemfaktoran

51 questions

Asesmen Formatif Kls-9 Topik Penjabaran & Pemfaktoran

quiz

Worksheet

•

9th Grade

Triangle sides & Trig ratios

50 questions

Triangle sides & Trig ratios

quiz

Worksheet

•

8th Grade