The vertices of Δ \Delta Δ PQR are P(-4, 3), Q(-2, 3), and R(1, -3). What are the coordinates of the vertices of Δ \Delta Δ P'Q'R' for a translation of T < 4 , − 5 > T_{<4,-5>} T < 4 , − 5 > ?

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

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

What is the translation shown?

T < − 5 , 2 > T_{<-5,\ 2>} T < − 5 , 2 >

T < 5 , − 2 > T_{<5,\ -2>} T < 5 , − 2 >

T < − 5 , − 2 > T_{<-5,\ -2>} T < − 5 , − 2 >

The vertices of Δ \Delta Δ ABC are A(2, -2), B(-3, -2), and C(-1, 3). What are the coordinates of the vertices of Δ \Delta Δ A'B'C' for a rotation of r ( 90 ° , O ) r_{\left(90\degree,\ O\right)} r ( 9 0 ° , O ) . Hint: r ( 90 ° , O ) ( x , y ) → ( − y , x ) r_{\left(90\degree,\ O\right)}(x,\ y)\rightarrow(-y,\ x) r ( 9 0 ° , O ) ( x , y ) → ( − y , x )

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

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

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

The vertices of Δ \Delta Δ ABC are A(2, -2), B(-3, -2), and C(-1, 3). What are the coordinates of the vertices of Δ \Delta Δ A'B'C' for a rotation of r ( 270 ° , O ) r_{\left(270\degree,\ O\right)} r ( 2 7 0 ° , O ) . Hint: r ( 270 ° , O ) ( x , y ) → ( y , − x ) r_{\left(270\degree,\ O\right)}(x,\ y)\rightarrow(y,\ -x) r ( 2 7 0 ° , O ) ( x , y ) → ( y , − x )

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

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

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

What is a glide reflection for the transformation shown?

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

T < 0 , 5 > ∘ R y − a x i s T_{<0,\ 5>}\circ\ R_{y-axis} T < 0 , 5 > ∘ R y − a x i s

T < 5 , 0 > ∘ R x − a x i s T_{<5,\ 0>}\circ\ R_{x-axis} T < 5 , 0 > ∘ R x − a x i s

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

180 ° 180\degree 1 8 0 ° rotation about the center

Reflection across the vertical line through the center

Reflection across the horizontal line through the center

90 ° 90\degree 9 0 ° rotation about the center

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

180 ° 180\degree 1 8 0 ° rotational symmetry about the center of the figure.

Reflection across the horizontal line through the center.

Reflection across the vertical line through the center.

90 ° 90\degree 9 0 ° rotational symmetry about the center of the figure.

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

T 〈 5 , − 5 〉 T_{〈5,−5〉} T 〈 5 , − 5 〉

T 〈 − 5 , 5 〉 T_{〈−5,5〉} T 〈 − 5 , 5 〉

Which of the descriptions is true for the graph?

△A″B″C″ is T 〈 − 5 , 0 〉 T_{〈−5,0〉} T 〈 − 5 , 0 〉 (△A′B′C′)

△A″B″C″ is ( T 〈 − 5 , 0 〉 T_{〈−5,0〉} T 〈 − 5 , 0 〉 ∘ R x − a x i s R_{x-axis} R x − a x i s ) (△A′B′C′)

△A″B″C″ is R x − a x i s R_{x-axis} R x − a x i s (△A′B′C′)

△A″B″C″ is r 90 ° r_{90°} r 9 0 ° (△A′B′C′)

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

T 〈 5 , − 3 〉 T_{〈5,−3〉} T 〈 5 , − 3 〉

T 〈 − 5 , 3 〉 T_{〈−5,3〉} T 〈 − 5 , 3 〉

T 〈 0 , 5 〉 T_{〈0,5〉} T 〈 0 , 5 〉

T 〈 − 5 , 0 〉 T_{〈−5,0〉} T 〈 − 5 , 0 〉

Which of the following does a rigid motion preserve?

side lengths and angle measures

neither side lengths nor angle measures

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)

R x − a x i s R_{x-axis} R x − a x i s (x, y) = (x, −y)

R y = − x R_{y=−x} R y = − x (x, y) = (−y, −x)

R y = − x R_{y=−x} R y = − x (x, y) = (y, x)

R y − a x i s R_{y-axis} R y − a x i s (x, y) = (−x, y)

What are the vertices of △A’B’C’ produced by T 〈 − 3 , 6 〉 T_{〈−3,6〉} T 〈 − 3 , 6 〉 (△ABC) = △A’B’C’?

A’(0, 6), B’(0, 4), C’(−3, 3)

A’(6, 6), B’(6, 4), C’(3, 3)

A’(0, −6), B’(0, −8), C’(−3, 9)

A’(6, −6), B’(6, −8), C’(3, 9)

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

T 〈 − 9 , − 2 〉 T_{〈−9,−2〉} T 〈 − 9 , − 2 〉 (△ABC) = △DEF

T 〈 9 , 2 〉 T_{〈9,2〉} T 〈 9 , 2 〉 (△ABC) = △DEF

T 〈 9 , − 2 〉 T_{〈9,−2〉} T 〈 9 , − 2 〉 (△ABC) = △DEF

T 〈 − 9 , 2 〉 T_{〈−9,2〉} T 〈 − 9 , 2 〉 (△ABC) = △DEF

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

( r ( 45 ° , A ) ∘ r ( − 120 ° , B ) ) ( A ) (r_{(45°,\ A)}\ ∘\ r_{(−120°,\ B)})(A) ( r ( 4 5 ° , A ) ∘ r ( − 1 2 0 ° , B ) ) ( A )

( r ( 120 ° , B ) ∘ r ( − 45 ° , A ) ) ( A ) (r_{(120°,\ B)\ }∘\ r_{(−45°,\ A)})(A) ( r ( 1 2 0 ° , B ) ∘ r ( − 4 5 ° , A ) ) ( A )

( r ( − 45 ° , A ) ∘ r ( 120 ° , B ) ) ( A ) (r_{(−45°,\ A)}\ ∘\ r_{(120°,\ B)})(A) ( r ( − 4 5 ° , A ) ∘ r ( 1 2 0 ° , B ) ) ( A )

( r ( − 120 ° , B ) ∘ r ( 45 ° , A ) ) ( A ) (r_{(−120°,\ B)\ }∘\ r_{(45°,\ A)})(A) ( r ( − 1 2 0 ° , B ) ∘ r ( 4 5 ° , A ) ) ( A )

Which rotation maps the figure onto itself?

r ( 180 ° , P ) r_{(180°,\ P)} r ( 1 8 0 ° , P )

r ( 45 ° , P ) r_{(45°,\ P)} r ( 4 5 ° , P )

r ( 90 ° , P ) r_{(90°,\ P)} r ( 9 0 ° , P )

r ( 270 ° , P ) r_{(270°,\ P)} r ( 2 7 0 ° , P )

Topic 3 Study Guide

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Mathematics

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37 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

rotation

translation

reflection

rigid motion

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

rigid motion

line of symmetry

compositions

preimages

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

line of symmetry

line of reflection

image

glide reflection

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

glide reflection

rotation

image

translation

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

preimage

image

reflection

line of reflection

Tags

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The result of a transformation is called the _______.

image

preimage

rigid motion

glide reflection

Tags

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Does the transformation appear to be a rigid motion?

Yes

Answer explanation

Rigid motions maintain angle measure and side length so this is definitely a rigid motion!

Tags

CCSS.HSG.CO.B.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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?

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

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

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

None of the above

Answer explanation

A reflection over the y axis has the rule:
(x, y) -> (-x, y)
Let's apply that rule to each coordinate:
(-3, 2) -> (3, 2)
(-1, -3) -> (1, -3)
(4, 3) -> (-4, 3)

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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?

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

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

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

None of the above

Answer explanation

A reflection over the x axis has the rule:
(x, y) -> (x, -y)
Let's apply that rule to each coordinate:
(-3, 2) -> (-3, -2)
(-1, -3) -> (-1, 3)
(4, 3) -> (4, -3)

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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 $T_{<-3,\ 2>}$ ?

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

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

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

None of the above

Answer explanation

This translation rule tells us we have to move each points to the left 3 units and up 2 units. So we subtract 3 from the x value and add 2 to the y value.
Let's apply this rule to each coordinate:
(-4, 3) -> (-4 - 3, 3 + 2) -> (-7, 5)
(-2, 3) -> (-2 - 3, 3 + 2) -> (-5, 5)
(1, -3) -> (1 - 3, -3 + 2) -> (-2, -1)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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Topic 3 Study Guide

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

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

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

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

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

The result of a transformation is called the _______.

Does the transformation appear to be a rigid motion?

Rigid motions maintain angle measure and side length so this is definitely a rigid motion!

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

A reflection over the y axis has the rule:(x, y) -> (-x, y)Let's apply that rule to each coordinate:(-3, 2) -> (3, 2)(-1, -3) -> (1, -3)(4, 3) -> (-4, 3)

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

A reflection over the x axis has the rule:(x, y) -> (x, -y)Let's apply that rule to each coordinate:(-3, 2) -> (-3, -2)(-1, -3) -> (-1, 3)(4, 3) -> (4, -3)

The vertices of Δ\DeltaΔ PQR are P(-4, 3), Q(-2, 3), and R(1, -3). What are the coordinates of the vertices of Δ\DeltaΔ P'Q'R' for a translation of T<−3, 2>T_{<-3,\ 2>}T<−3, 2>​ ?

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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 reflection over the y axis has the rule:
(x, y) -> (-x, y)
Let's apply that rule to each coordinate:
(-3, 2) -> (3, 2)
(-1, -3) -> (1, -3)
(4, 3) -> (-4, 3)

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 reflection over the x axis has the rule:
(x, y) -> (x, -y)
Let's apply that rule to each coordinate:
(-3, 2) -> (-3, -2)
(-1, -3) -> (-1, 3)
(4, 3) -> (4, -3)

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 $T_{<-3,\ 2>}$ ?