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Lesson: Combining Transformations

In this lesson, we will learn how to identify a set of transformations that are applied to a specified figure.

Worksheet • 11 Questions

Q1:

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 .

  • Aa 9 0 ∘ clockwise rotation about the origin
  • Ba dilation from point ( 0 , 3 ) by a scale factor of 2
  • C a 9 0 ∘ counterclockwise rotation about the origin
  • Da dilation from the origin by a scale factor of 2
  • E a 2 7 0 ∘ clockwise rotation about the origin

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 , 3 ) by a scale factor of 2
  • Ca dilation from the origin by a scale factor of 3
  • D a 1 8 0 ∘ clockwise rotation about point ( 0 , 6 )
  • E a 1 8 0 ∘ clockwise rotation about point ( 0 , 5 )

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:

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

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

Q3:

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 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 1 8 0 ∘ rotation about point 𝐷
  • Ba translation two right and eight down
  • Ca 9 0 ∘ clockwise rotation about point 𝐷
  • Da translation four left
  • Ea 9 0 ∘ counterclockwise rotation about point 𝐷

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

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

Q4:

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

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

Q5:

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

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

Q6:

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

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

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

Q7:

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

Q8:

Starting with triangle 𝐴 ( 2 , 1 ) , 𝐡 ( 9 , 4 ) , and 𝐢 ( 9 , 6 ) , apply the transformations: 1. reflect in the 𝑦 -axis, 2. reflect in the π‘₯ -axis, and 3. translate by 5 units right and 5 units up. What are the images of the vertices?

  • A 𝐴 β€² ( 3 , 4 ) , 𝐡 β€² ( βˆ’ 4 , 1 ) , 𝐢 β€² ( βˆ’ 4 , βˆ’ 1 )
  • B 𝐴 β€² ( 7 , 4 ) , 𝐡 β€² ( 1 4 , 1 ) , 𝐢 β€² ( βˆ’ 4 , βˆ’ 1 )
  • C 𝐴 β€² ( 3 , 4 ) , 𝐡 β€² ( βˆ’ 4 , 1 ) , 𝐢 β€² ( βˆ’ 9 , βˆ’ 6 )
  • D 𝐴 β€² ( 7 , 6 ) , 𝐡 β€² ( βˆ’ 4 , 1 ) , 𝐢 β€² ( βˆ’ 4 , 1 1 )
  • E 𝐴 β€² ( 3 , 4 ) , 𝐡 β€² ( βˆ’ 4 , 9 ) , 𝐢 β€² ( βˆ’ 4 , 1 1 )

Q9:

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

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 1 8 0 ∘ rotation about 𝐹
  • Ca 9 0 ∘ clockwise rotation about 𝐸
  • Da translation two up
  • Ea 9 0 ∘ clockwise 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 up
  • Ba translation three left and two down
  • Ca translation two left and three up
  • Da translation two right and three down
  • Ea translation three right and two 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

Q10:

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 no
  • B yes

Q11:

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