Worksheet: Rotations about a Point

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In this worksheet, we will practice identifying the rotation of a shape about a point and deducing the image of a polygon after rotating about one of its vertices.

Q1:

What kind of transformation is shown in the figure?

  • Aa rotation
  • Ba reflection
  • Ca translation

Q2:

Find the new positions of the given triangle’s vertices after rotating it 180∘ counterclockwise about 𝐿.

  • A 𝐿 β€² ( 5 , 4 ) , 𝑀 β€² ( 2 , 3 ) , 𝑁 β€² ( 4 , 1 )
  • B 𝐿 β€² ( 5 , 4 ) , 𝑀 β€² ( 3 , 1 ) , 𝑁 β€² ( 1 , 3 )
  • C 𝐿 β€² ( βˆ’ 5 , βˆ’ 4 ) , 𝑀 β€² ( βˆ’ 8 , βˆ’ 5 ) , 𝑁 β€² ( βˆ’ 6 , βˆ’ 7 )
  • D 𝐿 β€² ( 5 , 4 ) , 𝑀 β€² ( 1 3 , 9 ) , 𝑁 β€² ( 1 1 , 1 1 )

Q3:

Where does a rotation through 180∘ about 𝑀 send the segment 𝐹𝐴?

  • A 𝐢 𝐷
  • B 𝐴 𝐡
  • C 𝐷 𝐸
  • D 𝐸 𝐹

Q4:

Isabella went on a hike in the woods. She was walking northeast along a trail. When she got to a fork in the trail, she started walking southeast. Fully describe the rotation she made at the fork in the trail.

  • ARotation by 90∘ anticlockwise
  • BRotation by 90∘ clockwise
  • CRotation by 180∘ anticlockwise
  • DRotation by 45∘ clockwise
  • ERotation by 45∘ anticlockwise

Q5:

Sophia went on a hike in the woods. She was walking northeast along a trail. When she got to a fork in the trail, she started walking northwest. Fully describe the rotation she made at the fork in the trail.

  • ARotation by 45∘ counterclockwise
  • BRotation by 45∘ clockwise
  • CRotation by 90∘ clockwise
  • DRotation by 180∘ clockwise
  • ERotation by 90∘ counterclockwise

Q6:

Jennifer went on a hike in the woods. She was walking southwest along a trail. When she got to a fork in the trail, she started walking northwest. Fully describe the rotation she made at the fork in the trail.

  • ARotation by 90∘ counterclockwise
  • BRotation by 45∘ clockwise
  • CRotation by 90∘ clockwise
  • DRotation by 180∘ counterclockwise
  • ERotation by 45∘ counterclockwise

Q7:

Elizabeth and her family are camping at the lake. Elizabeth and her sister walk to the jetty on the lake. The last sign reads β€œJETTY”, but Elizabeth notices the first T is upside down. Is the first T a translation, reflection, or rotation of the second T?

  • Areflection
  • Brotation
  • Ctranslation

Q8:

Find the new positions of the given triangle’s vertices after rotating it 90∘ clockwise about 𝐿.

  • A 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 4 , βˆ’ 2 ) , 𝑁 β€² ( 7 , 2 )
  • B 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 2 , 4 ) , 𝑁 β€² ( βˆ’ 1 , 0 )
  • C 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 3 , 1 ) , 𝑁 β€² ( βˆ’ 1 , 4 )
  • D 𝐿 β€² ( 1 , βˆ’ 3 ) , 𝑀 β€² ( 2 , βˆ’ 6 ) , 𝑁 β€² ( 5 , βˆ’ 2 )
  • E 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 9 , 3 ) , 𝑁 β€² ( 5 , 6 )

Q9:

Find the new positions of the given triangle’s vertices after rotating it 90∘ clockwise about 𝐿.

  • A 𝐿 β€² ( 1 , 2 ) , 𝑀 β€² ( 2 , βˆ’ 1 ) , 𝑁 β€² ( 5 , 1 )
  • B 𝐿 β€² ( 1 , 2 ) , 𝑀 β€² ( 0 , 5 ) , 𝑁 β€² ( βˆ’ 3 , 3 )
  • C 𝐿 β€² ( 1 , 2 ) , 𝑀 β€² ( 3 , 1 ) , 𝑁 β€² ( 1 , 4 )
  • D 𝐿 β€² ( 2 , βˆ’ 1 ) , 𝑀 β€² ( 3 , βˆ’ 4 ) , 𝑁 β€² ( 6 , βˆ’ 2 )
  • E 𝐿 β€² ( 1 , 2 ) , 𝑀 β€² ( 5 , 5 ) , 𝑁 β€² ( 3 , 8 )

Q10:

Find the new positions of the given triangle’s vertices after rotating it 90∘ clockwise about 𝐿.

  • A 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 4 , βˆ’ 2 ) , 𝑁 β€² ( 8 , βˆ’ 2 )
  • B 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 2 , 4 ) , 𝑁 β€² ( βˆ’ 2 , 4 )
  • C 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 3 , 1 ) , 𝑁 β€² ( 3 , 5 )
  • D 𝐿 β€² ( 1 , βˆ’ 3 ) , 𝑀 β€² ( 2 , βˆ’ 6 ) , 𝑁 β€² ( 6 , βˆ’ 6 )
  • E 𝐿 β€² ( 3 , 1 ) , 𝑀 β€² ( 9 , 3 ) , 𝑁 β€² ( 9 , 7 )

Q11:

Where does a rotation through 36∘ about 𝑀 send the segment 𝐹𝐺?

  • A 𝐺 𝐻
  • B 𝐸 𝐹
  • C 𝐡 𝐢
  • D 𝑁 𝑃

Q12:

Where does a rotation through βˆ’60∘ about 𝑀 send the segment 𝐷𝐸?

  • A 𝐢 𝐷
  • B 𝐴 𝐡
  • C 𝐡 𝐢
  • D 𝐹 𝐴

Q13:

Where does a rotation through 225∘ about 𝑀 send the segment 𝐴𝐡?

  • A 𝐹 𝐺
  • B 𝐡 𝐢
  • C 𝐻 𝐴
  • D 𝐸 𝐹

Q14:

What type of transformation is the following?

  • Areflection
  • Btranslation
  • Crotation

Q15:

Which transformation can turn the letter d into p?

  • Atranslation
  • Brotation
  • Creflection

Q16:

Which transformation can turn the letter Z into N?

  • Areflection
  • Btranslation
  • Crotation

Q17:

Which of the following represents a rotation of the shaded figure?

  • A
  • B
  • C
  • D

Q18:

The figure shows a regular polygon. Where is the point 𝐡 moved to after a rotation through 240∘?

  • A 𝐹
  • B 𝐻
  • C 𝑁
  • D 𝐷

Q19:

Find all capital letters in WISCONSIN that look the same after being rotated 180∘.

  • AI, C, O, and N
  • BW and C
  • CI, S, and O
  • DI, S, C, O, and N
  • EI, S, O, and N

Q20:

β–³ 𝐴 𝐡 β€² 𝐢 β€² is the image of △𝐴𝐡𝐢 by a counterclockwise rotation of π‘₯∘ about 𝐴. Find π‘₯.

Q21:

What is the image of △𝐢𝐷𝑀 after a βˆ’108∘ rotation?

  • A β–³ 𝐴 𝐡 𝑀
  • B β–³ 𝑃 𝐴 𝑀
  • C β–³ 𝐹 𝐺 𝑀
  • D β–³ 𝐸 𝐹 𝑀

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