Quiz about Compositions of Transformations

Question 1

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

Accepted Answer

Reflection over x-axis, then Rotation of 90 Degrees

Answer

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

Answer

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

Answer

Rotation of 90 Degrees, then Reflection over x-axis

Question 2

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

Accepted Answer

Orange Triangle

Answer

Green Triangle

Answer

Blue Triangle

Answer

Red Triangle

Question 3

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

Accepted Answer

Rotation of 90 Degrees, then reflection over x-axis

Answer

Reflection x-axis, then rotation of 180 Degrees

Answer

Reflection over y-axis, then rotation of 90 Degrees

Answer

Rotation of 180 Degrees, then reflection over y-axis

Question 4

A double reflection over the x- and y-axes is the same as a ____________ of ______.

Accepted Answer

Rotation of 180 Degrees

Answer

Rotation of 90 Degrees

Answer

Reflection over the x-axis

Answer

Reflection over the y-axis

Question 5

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

Accepted Answer

Reflection across the x-axis

Answer

90^o clockwise rotation

Answer

90^o counter clockwise rotation

Answer

Reflection across the y-axis

Question 6

A transformation in which a second transformation is performed on a image of a first transformation is called

Accepted Answer

composition of transformation

Answer

translation

Answer

rigid motion

Answer

reflection

Question 7

What are the coordinates of point A' , the image of point A(-4, 1) after the composite transformation R₉₀ o r_y=x where the origin is the center of rotation?

Accepted Answer

(4, 1)

Answer

(-1, -4)

Answer

(-4, -1)

Answer

(1, 4)

Question 8

The coordinates of triangle JRB are ,J(1, -2) , R(-3, 6) and B(4, 5) . What are the coordinates of the vertices of its image after the transformation T_{2, -1} o r_y-axis ?

Accepted Answer

(1, -3), (5, 5), (-2, 4)

Answer

(3, 1), (-1, -7), (6, -6)

Answer

(3, -3), (-1, 5), (6, 4)

Answer

(-1, -2), (3, 6), (-4, 5)

Question 9

If the coordinates of point P are (2, -3) , then R₉₀ o R₁₈₀is

Accepted Answer

(-3, -2)

Answer

(-2, 3)

Answer

(-2, -3)

Answer

(3, -2)

Question 10

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

Accepted Answer

translate 5 down and 1 left, then reflect over y

Answer

translate 5 up and 1 left then reflect over y

Answer

reflect over y=x then translate left 8

Answer

reflect over x then rotate 90 clockwise

Question 11

Name the series of transformations that maps ABC onto DEF

Accepted Answer

reflect over x then translate left 6 up 1

Answer

reflect over y then translate down 6 left 1

Answer

translate right 6 down 1, then reflect over x

Answer

rotate 90 clockwise then reflect over y

Question 12

Which of the following describes the sequence of transformations shown?

Accepted Answer

Translate up and then rotate 90 degrees about the origin.

Answer

Reflect across the x-axis and then rotate -90 degrees around the origin

Answer

Rotate -90 degrees around the origin and then translate down.

Answer

Reflect across the x-axis and then reflect across the y-axis.

Question 13

The coordinates of triangle JRB are ,J(1, -2) , R(-3, 6) and B(4, 5) . What are the coordinates of the vertices of its image after the transformation T_{2, -1} o R_y-axis ?

Accepted Answer

(1, -3), (5, 5), (-2, 4)

Answer

(3, 1), (-1, -7), (6, -6)

Answer

(3, -3), (-1, 5), (6, 4)

Answer

(-1, -2), (3, 6), (-4, 5)

Question 14

What are the coordinates of point A' , the image of point A(-4, 1) after the composite transformation r₉₀ o R_y=2 where the origin is the center of rotation?

Accepted Answer

(-3, -4)

Answer

(-4, -3)

Answer

(3, 4)

Answer

(4, 3)

Question 15

Triangle XYZ has vertices X(-2, 2) Y(3, 2) and Z(-5, -6). Rotate the figure 180 degrees, translate it 2 units up and 4 units right, then dilate by a scale factor of 2. What are the new coordinates?

Accepted Answer

X'''(12,0) Y'''(2,0) Z'''(18,16)

Answer

X'''(8,4) Y'''(-2,4) Z'''(14,20)

Answer

X'''(12,0) Y'''(2,0) Z'''(3, 4)

Answer

X'''(8,4) Y'''(2,0) Z'''(14,20)

Question 16

What is the second step in the composition?

R_D,90(r_y-axis(T_2,-3(triangle ABC)))

Accepted Answer

Translation right 2, down 3

Answer

Translation up 2, left 3

Answer

Draw triangle ABC

Answer

Rotate about point D 90 degrees

Answer

Reflect over y-axis

Question 17

What is the third step in the composition?

R_D,90(r_y-axis(T_2,-3(triangle ABC)))

Accepted Answer

Reflect over y-axis

Answer

Translation up 2, left 3

Answer

Translation right 2, down 3

Answer

Draw triangle ABC

Answer

Rotate about point D 90 degrees

Question 18

What goes last in the composition?

R_D,90(r_y-axis(T_2,-3(triangle ABC)))

Accepted Answer

Rotate about point D 90 degrees

Answer

Translation up 2, left 3

Answer

Translation right 2, down 3

Answer

Draw triangle ABC

Answer

Reflect over y-axis

Question 19

What goes first in the composition?

R_D,90(r_y-axis(T_2,-3(triangle ABC)))

Accepted Answer

Draw triangle ABC

Answer

Translation up 2, left 3

Answer

Translation right 2, down 3

Answer

Rotate about point D 90 degrees

Answer

Reflect over y-axis

Question 20

Which would be the correct notation for the composition of transformations from blue to red to green?

Accepted Answer

T<0,-4>^o R_{y axis}

Answer

T<-4,0>^o R_{y axis}

Answer

R_{y axis}o T<0,-4>

Answer

R_{x axis}o R_{y axis}

Question 21

Find the image of A( -3, 5) after translating (x,y) --> (x-6 , y -1) then reflecting across the line x= -1

Accepted Answer

( 7, 4)

Answer

( 4, 7)

Answer

(-5, 4)

Answer

(4, -5)

Question 22

Find the image of A( -3, 5) after translating (x,y) --> (x , y-4) then reflecting across the y-axis

Accepted Answer

(3,1)

Answer

(3, -1)

Answer

(-1, 5)

Answer

(-1, 3)

Question 23

Combine the transformations (x, y)--> (x+14, y+1) and (x,y)-->(x-3, y+8)

Accepted Answer

(x, y)--> (x+11, y+9)

Answer

(x, y)--> (x-17, y-7)

Compositions of Transformations

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