Free Printable Topic 3 Study Guide

1.

A(n) _______________ is a transformation about a point with a given angle measure.

a)

rotation

b)

translation

c)

reflection

d)

rigid motion

2.

Reflections, translations, rotations, and glide reflections are the four types of _____________.

a)

rigid motion

b)

line of symmetry

c)

compositions

d)

preimages

3.

A line that a figure is reflected across so that it maps onto itself is called a(n) ____________.

a)

line of symmetry

b)

line of reflection

c)

image

d)

glide reflection

4.

The composition of a reflection and a translation is called a(n) _______________.

a)

glide reflection

b)

rotation

c)

image

d)

translation

5.

The set of points that a transformation acts on is called the ___________.

a)

preimage

b)

image

c)

reflection

d)

line of reflection

6.

The result of a transformation is called the _______.

a)

image

b)

preimage

c)

rigid motion

d)

glide reflection

7.

Does the transformation appear to be a rigid motion?

a)

Yes

b)

No

8.

The vertices of $\Delta$ HJK are H(-3, 2), J(-1, -3), and K(4, 3). What are the coordinates of the vertices of $\Delta$ H'J'K' for a reflection over the y-axis?

a)

H'(3, 2), J'(1, -3), K'(-4, 3)

b)

H'(-3, -2), J'(-1, 3), K'(4, -3)

c)

H'(3, -2), J'(1, 3), K'(4, 3)

d)

None of the above

9.

The vertices of $\Delta$ HJK are H(-3, 2), J(-1, -3), and K(4, 3). What are the coordinates of the vertices of $\Delta$ H'J'K' for a reflection over the x-axis?

a)

H'(3, 2), J'(1, -3), K'(-4, 3)

b)

H'(-3, -2), J'(-1, 3), K'(4, -3)

c)

H'(3, -2), J'(1, 3), K'(4, 3)

d)

None of the above

10.

The vertices of $\Delta$ PQR are P(-4, 3), Q(-2, 3), and R(1, -3). What are the coordinates of the vertices of $\Delta$ P'Q'R' for a translation of $T_{<-3,\ 2>}$ ?

a)

P'(-7, 5), Q'(-5, 5), R'(-2, -1)

b)

P'(-1, 1), Q'(1, 1), R'(4, -6)

c)

P'(-1, 5), Q'(-5, 1), R'(4, -1)

d)

None of the above

11.

The vertices of $\Delta$ PQR are P(-4, 3), Q(-2, 3), and R(1, -3). What are the coordinates of the vertices of $\Delta$ P'Q'R' for a translation of $T_{<4,-5>}$ ?

a)

P'(0, -2), Q'(2, -2), R'(5, -8)

b)

P'(-8, 8), Q'(-6, 8), R'(-3, 2)

c)

P'(0, 8), Q'(2, 8), R'(5, 2)

d)

None of the above

12.

What is the translation shown?

a)

$T_{<-5,\ 2>}$

b)

$T_{<5,\ -2>}$

c)

$T_{<-5,\ -2>}$

d)

None of the above

13.

The vertices of $\Delta$ ABC are A(2, -2), B(-3, -2), and C(-1, 3). What are the coordinates of the vertices of $\Delta$ A'B'C' for a rotation of $r_{\left(90\degree,\ O\right)}$ .
Hint: $r_{\left(90\degree,\ O\right)}(x,\ y)\rightarrow(-y,\ x)$

a)

A'(2, 2), B'(2, -3), C'(-3, -1)

b)

A'(2, 2), B'(-2, -3), C'(3, -1)

c)

A'(2, 2), B'(-3, 2), C'(-1, -3)

d)

None of the above

14.

The vertices of $\Delta$ ABC are A(2, -2), B(-3, -2), and C(-1, 3). What are the coordinates of the vertices of $\Delta$ A'B'C' for a rotation of $r_{\left(270\degree,\ O\right)}$ .
Hint: $r_{\left(270\degree,\ O\right)}(x,\ y)\rightarrow(y,\ -x)$

a)

A'(-2, -2), B'(-2, 3), C'(3, 1)

b)

A'(2, 2), B'(-2, -3), C'(3, -1)

c)

A'(2, 2), B'(-2, 3), C'(-3, -1)

d)

None of the above

15.

What is a glide reflection for the transformation shown?

a)

$T_{<0,\ 5>}\circ\ R_{x=\frac{1}{2}}$

b)

$T_{<0,\ 5>}\circ\ R_{y-axis}$

c)

$T_{<5,\ 0>}\circ\ R_{x-axis}$

d)

None of the above

16.

Describe the transformations that can be used to map the figure onto itself. Select ALL that apply.

a)

Reflection across the horizontal line through the center

b)

Reflection across the vertical line through the center

c)

$180\degree$ rotation about the center

d)

$90\degree$ rotation about the center

17.

Describe all symmetries of the figure. Select ALL that apply.

a)

Reflection across the horizontal line through the center.

b)

Reflection across the vertical line through the center.

c)

$180\degree$ rotational symmetry about the center of the figure.

d)

$90\degree$ rotational symmetry about the center of the figure.

18.

If this figure has rotational symmetry, give the angles of rotation. Select ALL that apply.

a)

$90\degree$

b)

$120\degree$

c)

$240\degree$

d)

$180\degree$

19.

What is a rule for the translation of △RST? Select all that apply.

a)

$T_{〈5,−5〉}$

b)

5 units down; 5 units right

c)

5 units up; 5 units left

d)

$T_{〈−5,5〉}$

20.

What rigid motion maps the solid-line figure onto the dotted line figure?

a)

reflection

b)

translation

c)

rotation

21.

Which of the descriptions is true for the graph?

a)

△A″B″C″ is $T_{〈−5,0〉}$ (△A′B′C′)

b)

△A″B″C″ is ( $T_{〈−5,0〉}$ ∘ $R_{x-axis}$ ) (△A′B′C′)

c)

△A″B″C″ is $R_{x-axis}$ (△A′B′C′)

d)

△A″B″C″ is $r_{90°}$ (△A′B′C′)

22.

Point P′(−3, 2) is the image of point P(3, 8) under a translation. What

is the image of (0, −6) under the

same translation?

a)

(−3, −4)

b)

(0, 6)

c)

(0, 10)

d)

(−6, −12)

23.

Which capital letters have one or more lines of symmetry? Select all that apply.

a)

V

b)

M

c)

N

d)

O

24.

The rule $T_{〈4,−1〉}$ is used for point (2, −7). Where is the translated point in the coordinate system?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

25.

If a figure is translated with the rule $T_{〈−5,3〉}$ , which translation moves the image back to the original position?

a)

$T_{〈5,−3〉}$

b)

$T_{〈−5,3〉}$

c)

$T_{〈0,5〉}$

d)

$T_{〈−5,0〉}$

26.

Find the lines of symmetry for the shape. Select all that apply.

a)

l

b)

m

c)

n

d)

o

27.

Find the lines of symmetry for the shape. Select all that apply.

a)

l

b)

m

c)

n

d)

o

28.

Which words have horizontal reflection symmetry? Select all that apply.

a)

BOOK

b)

POP

c)

CHECK

d)

SUCCEED

29.

Which of the following does a rigid motion preserve?

a)

side lengths only

b)

angle measures only

c)

side lengths and angle measures

d)

neither side lengths nor angle measures

30.

What is the rule used to transform △ABC to its image?

A(−3, 5), B(2, 8), C(−4, −5) and A’(−3, −5), B’(2, −8), C’(−4, 5)

a)

$R_{y=−x}$ (x, y) = (−y, −x)

b)

$R_{y=−x}$ (x, y) = (y, x)

c)

$R_{y-axis}$ (x, y) = (−x, y)

d)

$R_{x-axis}$ (x, y) = (x, −y)

31.

What are the vertices of △A’B’C’ produced by $T_{〈−3,6〉}$ (△ABC) = △A’B’C’?

a)

A’(0, 6), B’(0, 4), C’(−3, 3)

b)

A’(6, 6), B’(6, 4), C’(3, 3)

c)

A’(0, −6), B’(0, −8), C’(−3, 9)

d)

A’(6, −6), B’(6, −8), C’(3, 9)

32.

Suppose △DEF is the image of a translation of △ABC. If D is at (−6, −2), what translation rule maps △ABC to △DEF?

a)

$T_{〈9,2〉}$ (△ABC) = △DEF

b)

$T_{〈9,−2〉}$ (△ABC) = △DEF

c)

$T_{〈−9,2〉}$ (△ABC) = △DEF

d)

$T_{〈−9,−2〉}$ (△ABC) = △DEF

33.

$\overline{AB}$ is rotated 120° clockwise about B. Then $\overline{AB}$ is rotated 45° counterclockwise about A. What is the image of A as a composition of transformations?

a)

$(r_{(120°,\ B)\ }∘\ r_{(−45°,\ A)})(A)$

b)

$(r_{(−45°,\ A)}\ ∘\ r_{(120°,\ B)})(A)$

c)

$(r_{(−120°,\ B)\ }∘\ r_{(45°,\ A)})(A)$

d)

$(r_{(45°,\ A)}\ ∘\ r_{(−120°,\ B)})(A)$

34.

How many lines of symmetry does the pentagon have?

a)

0

b)

1

c)

3

d)

5

35.

What is the least angle of rotation that maps the pentagon onto itself?

a)

$90\degree$

b)

$72\degree$

c)

$60\degree$

d)

$45\degree$

36.

What reflections map the figure onto itself? Select all that apply.

a)

$R_m$

b)

$R_n$

37.

Which rotation maps the figure onto itself?

a)

$r_{(45°,\ P)}$

b)

$r_{(90°,\ P)}$

c)

$r_{(180°,\ P)}$

d)

$r_{(270°,\ P)}$

Topic 3 Study Guide

Total questions: 37

Worksheet time: 2hrs 42mins

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