Worksheet: Rotations about a Point

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.

  • A𝐿′(5,4), 𝑀′(2,3), 𝑁′(4,1)
  • B𝐿′(5,4), 𝑀′(3,1), 𝑁′(1,3)
  • C𝐿′(βˆ’5,βˆ’4), 𝑀′(βˆ’8,βˆ’5), 𝑁′(βˆ’6,βˆ’7)
  • D𝐿′(5,4), 𝑀′(13,9), 𝑁′(11,11)

Q3:

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

  • A𝐢𝐷
  • B𝐴𝐡
  • C𝐷𝐸
  • D𝐸𝐹

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.

  • A𝐿′(3,1), 𝑀′(4,βˆ’2), 𝑁′(7,2)
  • B𝐿′(3,1), 𝑀′(2,4), 𝑁′(βˆ’1,0)
  • C𝐿′(3,1), 𝑀′(3,1), 𝑁′(βˆ’1,4)
  • D𝐿′(1,βˆ’3), 𝑀′(2,βˆ’6), 𝑁′(5,βˆ’2)
  • E𝐿′(3,1), 𝑀′(9,3), 𝑁′(5,6)

Q9:

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

  • A𝐿′(1,2), 𝑀′(2,βˆ’1), 𝑁′(5,1)
  • B𝐿′(1,2), 𝑀′(0,5), 𝑁′(βˆ’3,3)
  • C𝐿′(1,2), 𝑀′(3,1), 𝑁′(1,4)
  • D𝐿′(2,βˆ’1), 𝑀′(3,βˆ’4), 𝑁′(6,βˆ’2)
  • E𝐿′(1,2), 𝑀′(5,5), 𝑁′(3,8)

Q10:

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

  • A𝐿′(3,1), 𝑀′(4,βˆ’2), 𝑁′(8,βˆ’2)
  • B𝐿′(3,1), 𝑀′(2,4), 𝑁′(βˆ’2,4)
  • C𝐿′(3,1), 𝑀′(3,1), 𝑁′(3,5)
  • D𝐿′(1,βˆ’3), 𝑀′(2,βˆ’6), 𝑁′(6,βˆ’6)
  • E𝐿′(3,1), 𝑀′(9,3), 𝑁′(9,7)

Q11:

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

  • A𝐺𝐻
  • B𝐸𝐹
  • C𝐡𝐢
  • D𝑁𝑃

Q12:

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

  • A𝐢𝐷
  • B𝐴𝐡
  • C𝐡𝐢
  • D𝐹𝐴

Q13:

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

  • A𝐹𝐺
  • B𝐡𝐢
  • C𝐻𝐴
  • D𝐸𝐹

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∘?

  • A𝐹
  • B𝐻
  • C𝑁
  • D𝐷

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:

△𝐴𝐡′𝐢′ 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△𝐴𝐡𝑀
  • B△𝑃𝐴𝑀
  • C△𝐹𝐺𝑀
  • D△𝐸𝐹𝑀

Q22:

In the figure, a rotation through 180∘ about 𝐢 maps △𝐢𝐴𝐡 onto △𝐢𝐴′𝐡′. If 𝐡𝐢=10.1cm, find the area of △𝐴𝐴′𝐡′ to the nearest hundredth.

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