Worksheet: Combining Transformations

In this worksheet, we will practice identifying a set of transformations that are applied to a specified figure.

Q1:

The triangle 𝐴 𝐡 𝐢 has been transformed onto triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² which has then been transformed onto triangle 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

Describe the single transformation that maps 𝐴 𝐡 𝐢 onto 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • Aa dilation from the point 𝐴 by a scale factor of 3
  • Ba dilation from the point 𝐷 by a scale factor of 2
  • Ca rotation of 9 0 ∘ clockwise about the point 𝐷
  • Da dilation from the point 𝐷 by a scale factor of 3
  • Ea rotation of 1 8 0 ∘ about the point 𝐷

Describe the single transformation that maps 𝐴 β€² 𝐡 β€² 𝐢 β€² onto 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa rotation of 1 8 0 ∘ about the point 𝐷
  • Ba rotation of 9 0 ∘ clockwise about the point 𝐷
  • Ca rotation of 1 8 0 ∘ about the point 𝐡
  • Da rotation of 1 8 0 ∘ about the point 𝐴
  • Ea rotation of 9 0 ∘ counterclockwise about the point 𝐷

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² similar?

  • Ano
  • Byes

Q2:

A shape 𝐹 has been reflected in the line 𝑦 = π‘₯ and then rotated 2 7 0 ∘ clockwise about the origin to 𝐹 β€² . Would 𝐹 and 𝐹 β€² be congruent?

  • A yes
  • B no

Q3:

In the given figure, triangle 𝐴 has been transformed to triangle 𝐡 . Which of the following sequences of transformations could have been used?

  • A a reflection in the π‘₯ -axis followed by a translation four right and four up
  • B a 9 0 ∘ rotation about the point ( βˆ’ 2 , βˆ’ 2 ) followed by a translation three right
  • C a 1 8 0 ∘ rotation about the origin followed by a translation three up
  • D a 1 8 0 ∘ rotation about the point ( βˆ’ 2 , 2 ) followed by a translation three right
  • Ea reflection in the line 𝑦 = 1 followed by a reflection in the π‘₯ -axis

Q4:

In the given figure, triangle 𝐴 has been transformed to triangle 𝐴 β€² by reflecting first in the 𝑦 -axis and then reflecting in the π‘₯ axis. What single transformation would have mapped 𝐴 to 𝐴 β€² ?

  • A a rotation about the origin of 9 0 ∘
  • B a reflection in the line 𝑦 = π‘₯
  • C a reflection in the 𝑦 -axis
  • D a rotation about the origin of 1 8 0 ∘
  • Ea rotation about the origin of 2 7 0 ∘

Q5:

𝐴 𝐡 𝐢 𝐷 is reflected in the π‘₯ -axis and then translated 5 units to the right. What is the image of point 𝐡 ?

  • A ( βˆ’ 6 , βˆ’ 7 )
  • B ( βˆ’ 7 , βˆ’ 6 )
  • C ( 2 , 6 )
  • D ( βˆ’ 2 , βˆ’ 6 )
  • E ( βˆ’ 6 , βˆ’ 2 )

Q6:

Starting with triangle 𝐴 ( 3 , 7 ) , 𝐡 ( 4 , 1 ) , and 𝐢 ( 8 , 7 ) , apply the transformations: 1. reflect in the 𝑦 -axis, 2. reflect in the π‘₯ -axis, and 3. translate by 3 units right and 3 units up. What are the images of the vertices?

  • A 𝐴 β€² ( 0 , βˆ’ 4 ) , 𝐡 β€² ( βˆ’ 1 , 4 ) , 𝐢 β€² ( βˆ’ 5 , 1 0 )
  • B 𝐴 β€² ( 0 , βˆ’ 4 ) , 𝐡 β€² ( βˆ’ 1 , 2 ) , 𝐢 β€² ( βˆ’ 8 , βˆ’ 7 )
  • C 𝐴 β€² ( 6 , 1 0 ) , 𝐡 β€² ( βˆ’ 1 , 2 ) , 𝐢 β€² ( βˆ’ 5 , 1 0 )
  • D 𝐴 β€² ( 0 , βˆ’ 4 ) , 𝐡 β€² ( βˆ’ 1 , 2 ) , 𝐢 β€² ( βˆ’ 5 , βˆ’ 4 )
  • E 𝐴 β€² ( 6 , βˆ’ 4 ) , 𝐡 β€² ( 7 , 2 ) , 𝐢 β€² ( βˆ’ 5 , βˆ’ 4 )

Q7:

The triangle 𝐴 𝐡 𝐢 has been transformed onto triangle 𝐴 𝐡 𝐢    which has then been transformed onto triangle 𝐴 𝐡 𝐢       then transformed onto 𝐴 𝐡 𝐢          as seen in the figure.

Describe the single transformation that would map 𝐴 𝐡 𝐢 onto 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • Aa 9 0 ∘ counterclockwise rotation about 𝐸
  • Ba 9 0 ∘ clockwise rotation about 𝐷
  • Ca 9 0 ∘ clockwise rotation about 𝐸
  • Da 9 0 ∘ counterclockwise rotation about 𝐷
  • Ea translation one left and three up

Describe the single transformation that would map 𝐴 β€² 𝐡 β€² 𝐢 β€² onto 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa reflection in the line βƒ–     βƒ— 𝐸 𝐹
  • Ba translation two up
  • Ca 9 0 ∘ clockwise rotation about 𝐹
  • Da 9 0 ∘ clockwise rotation about 𝐸
  • Ea 1 8 0 ∘ rotation about 𝐹

Describe the single transformation that would map 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² onto 𝐴 β€² β€² β€² 𝐡 β€² β€² β€² 𝐢 β€² β€² β€² .

  • Aa translation three left and two down
  • Ba translation two left and three up
  • Ca translation three left and two up
  • Da translation three right and two down
  • Ea translation two right and three down

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² β€² 𝐡 β€² β€² β€² 𝐢 β€² β€² β€² congruent?

  • Ano
  • Byes

Q8:

The triangle 𝐴 𝐡 𝐢 has been transformed onto triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² which has then been transformed onto triangle 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

Describe the single transformation that maps 𝐴 𝐡 𝐢 onto 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • Aa translation two down
  • Ba translation two up
  • Ca 9 0 ∘ rotation clockwise about point 𝐸
  • Da reflection in 𝐷 𝐸
  • Ea 9 0 ∘ rotation counterclockwise about point 𝐸

Describe the single transformation that maps 𝐴 β€² 𝐡 β€² 𝐢 β€² onto 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa dilation from the point 𝐸 by a scale factor of 2
  • Ba translation two down
  • Ca dilation from the point 𝐸 by a scale factor of 1 2
  • Da dilation from the point 𝐷 by a scale factor of 2
  • Ea translation two up

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² similar?

  • Ano
  • Byes

Q9:

The triangle 𝐴 𝐡 𝐢 has been transformed onto triangle 𝐴 𝐡 𝐢    which has then been transformed onto triangle 𝐴 𝐡 𝐢       .

Describe the single transformation that maps 𝐴 𝐡 𝐢 onto 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • A a 2 7 0 ∘ clockwise rotation about the origin
  • B a 9 0 ∘ counterclockwise rotation about the origin
  • Ca dilation from the origin by a scale factor of 2
  • Da 9 0 ∘ clockwise rotation about the origin
  • Ea dilation from point ( 0 , 3 ) by a scale factor of 2

Describe the single transformation that maps 𝐴 β€² 𝐡 β€² 𝐢 β€² onto 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa dilation from the origin by a scale factor of 2
  • B a 1 8 0 ∘ clockwise rotation about point ( 0 , 6 )
  • C a 1 8 0 ∘ clockwise rotation about point ( 0 , 5 )
  • Da dilation from the origin by a scale factor of 3
  • Ea dilation from point ( 0 , 3 ) by a scale factor of 2

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² similar?

  • Ano
  • Byes

Q10:

The triangle 𝐴 𝐡 𝐢 has been transformed onto triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² which has then been transformed onto triangle 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

Describe the single transformation that maps 𝐴 𝐡 𝐢 onto 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • Aa reflection in the π‘₯ -axis
  • Ba translation three up and one right
  • Ca reflection in the 𝑦 -axis
  • Da translation three right and one up
  • Ea translation two right and three up

Describe the single transformation that maps 𝐴 β€² 𝐡 β€² 𝐢 β€² onto 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa dilation from the origin by a scale factor of 2
  • Ba dilation from point ( 0 , 2 ) by a scale factor of 1 2
  • Ca translation one right and two up
  • Da translation one left and two up
  • Ea dilation from point ( 0 , 4 ) by a scale factor of 1 2

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² similar?

  • Ano
  • Byes

Q11:

The triangle 𝐴 𝐡 𝐢 has been transformed onto triangle 𝐴 𝐡 𝐢    which has then been transformed onto triangle 𝐴 𝐡 𝐢       as seen in the figure.

Describe the single transformation that would map 𝐴 𝐡 𝐢 to 𝐴 β€² 𝐡 β€² 𝐢 β€² .

  • Aa rotation of 1 8 0 ∘ about 𝐸
  • Ba rotation of 1 8 0 ∘ about 𝐷
  • Ca rotation of 9 0 ∘ clockwise about point 𝐷
  • Da reflection in the line βƒ–     βƒ— 𝐷 𝐸
  • Ea rotation of 9 0 ∘ clockwise about point 𝐸

Describe the single transformation that would map 𝐴 β€² 𝐡 β€² 𝐢 β€² to 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² .

  • Aa rotation of 9 0 ∘ clockwise about point 𝐹
  • Ba rotation of 9 0 ∘ clockwise about point 𝐸
  • Ca translation two right
  • Da rotation of 9 0 ∘ counterclockwise about point 𝐹
  • Ea rotation of 9 0 ∘ counterclockwise about point 𝐸

Hence, are triangles 𝐴 𝐡 𝐢 and 𝐴 β€² β€² 𝐡 β€² β€² 𝐢 β€² β€² congruent?

  • Ano
  • Byes

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