Worksheet: Rotations in the First Quadrant

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

Q1:

What kind of transformation is shown in the figure?

  • Aa translation
  • Ba reflection
  • Ca rotation

Q2:

Find the new positions of the given triangle’s vertices after rotating it 1 8 0 ∘ anticlockwise about 𝐿 .

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

Q3:

Where does a rotation through 1 8 0 ∘ about 𝑀 send the segment 𝐹 𝐴 ?

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

Q4:

Nada went on a hike in the woods. The arrow on the compass pointed northeast. After Nada made a turn on the trail, the compass pointed southeast. Describe the arrow’s transformation.

  • Arotation by 1 8 0 ∘ anticlockwise
  • Brotation by 9 0 ∘ anticlockwise
  • Crotation by 4 5 ∘ anticlockwise
  • Drotation by 9 0 ∘ clockwise
  • Erotation by 4 5 ∘ clockwise

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.

  • A Rotation by 1 8 0 ∘ clockwise
  • B Rotation by 9 0 ∘ clockwise
  • CRotation by 4 5 ∘ counterclockwise
  • D Rotation by 9 0 ∘ counterclockwise
  • ERotation by 4 5 ∘ clockwise

Q6:

Engy went on a hike in the woods. The arrow on the compass pointed southwest. When Engy made a turn on the trail, the compass pointed northwest. Describe the arrow’s transformation.

  • Arotation by 1 8 0 ∘ anticlockwise
  • Brotation by 9 0 ∘ anticlockwise
  • Crotation by 4 5 ∘ anticlockwise
  • Drotation by 9 0 ∘ clockwise
  • Erotation by 4 5 ∘ clockwise

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?

  • A translation
  • B reflection
  • C rotation

Q8:

Find the new positions of the given triangle’s vertices after rotating it 9 0 ∘ clockwise about 𝐿 .

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

Q9:

Find the new positions of the given triangle’s vertices after rotating it 9 0 ∘ clockwise about 𝐿 .

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

Q10:

Find the new positions of the given triangle’s vertices after rotating it 9 0 ∘ clockwise about 𝐿 .

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

Q11:

Where does a rotation through 3 6 ∘ about 𝑀 send the segment 𝐹 𝐺 ?

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

Q12:

Where does a rotation through βˆ’ 6 0 ∘ about 𝑀 send the segment 𝐷 𝐸 ?

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

Q13:

Where does a rotation through 2 2 5 ∘ about 𝑀 send the segment 𝐴 𝐡 ?

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

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