Lesson Worksheet: Rotations Mathematics

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In this worksheet, we will practice drawing the rotation of a shape in the coordinate plane around the origin.

Q1:

What is the image of the point (−3,14) after a rotation about the origin through an angle of 90∘?

  • A(−3,−14)
  • B(−14,3)
  • C(3,14)
  • D(−14,−3)

Q2:

Rotate triangle 𝐴𝐵𝐶180∘ clockwise about the origin, and state the coordinates of the image.

  • A(2,0), (1,−2), (1,3)
  • B(−2,0), (1,−2), (1,−3)
  • C(0,2), (−2,−1), (3,−1)
  • D(−2,0), (1,2), (1,−3)
  • E(2,0), (−1,−2), (−1,3)

Q3:

A triangle graphed on the coordinate plane has a vertex at (6,0). Which of the following rotations would move the vertex to point (0,6)?

  • A90∘ clockwise around the origin
  • B90∘ counterclockwise around the origin
  • C180∘ clockwise or counterclockwise around the origin

Q4:

Describe the single transformation that would map triangle 𝐴𝐵𝐶 onto triangle 𝐴′𝐵′𝐶′ in the given figure.

  • AA rotation of 270∘ counterclockwise about 𝐷
  • BA rotation of 270∘ clockwise about 𝐸
  • CA rotation of 90∘ clockwise about 𝐸
  • DA rotation of 90∘ clockwise about 𝐷
  • EA rotation of 90∘ counterclockwise about 𝐷

Q5:

A triangle has its vertices at the points (2, 1), (3, 2) and (2, 4). The triangle is rotated 90∘ counterclockwise about the origin. At which of the following coordinates will the image have its vertices?

  • A(−1,2),(−2,3), and (−4,2)
  • B(1,2),(2,3), and (2,−4)
  • C(−2,1),(−2,3), and (4,−2)
  • D(2,−1),(3,−2), and (2,−4)
  • E(−1,2),(2,3), and (2,−4)

Q6:

Rotate the given triangle about the origin 90∘ clockwise. Which of the following sets of coordinates will be the vertices of the image?

  • A(2,1),(4,2), and (2,5)
  • B(1,2),(2,4), and (5,2)
  • C(−2,1),(−2,4), and (−5,2)
  • D(1,−2),(4,−2), and (2,−5)
  • E(2,−1),(4,−2), and (2,−5)

Q7:

Given that 𝑋(4,−2), 𝑌(8,−3), and 𝑍(5,−8) form a triangle, determine the images of its vertices after a clock wise rotation of 180∘ about the origin.

  • A𝑋′(2,−4), 𝑌′(3,−8), 𝑍′(8,−5)
  • B𝑋′(−4,2), 𝑌′(3,−8), 𝑍′(−5,8)
  • C𝑋′(2,−4), 𝑌′(−8,3), 𝑍′(−5,8)
  • D𝑋′(−4,2), 𝑌′(−8,3), 𝑍′(8,−5)
  • E𝑋′(−4,2), 𝑌′(−8,3), 𝑍′(−5,8)

Q8:

Determine the coordinates of the vertices’ images of triangle 𝐴𝐵𝐶 after a counterclockwise rotation of 270∘ around the origin.

  • A𝐴′(−3,7), 𝐵′(3,−4), 𝐶′(−5,6)
  • B𝐴′(−3,7), 𝐵′(−4,3), 𝐶′(6,−5)
  • C𝐴′(7,−3), 𝐵′(−4,3), 𝐶′(−5,6)
  • D𝐴′(7,−3), 𝐵′(3,−4), 𝐶′(6,−5)
  • E𝐴′(−3,7), 𝐵′(−4,3), 𝐶′(−5,6)

Q9:

Determine the coordinates of the vertices’ images of triangle 𝐴𝐵𝐶 after a counterclockwise rotation of 180∘ around the origin.

  • A𝐴′(8,−7), 𝐵′(3,−7), 𝐶′(4,−3)
  • B𝐴′(−7,8), 𝐵′(−7,3), 𝐶′(−3,4)
  • C𝐴′(8,−7), 𝐵′(−7,3), 𝐶′(4,−3)
  • D𝐴′(8,−7), 𝐵′(3,−7), 𝐶′(−3,4)
  • E𝐴′(−7,8), 𝐵′(3,−7), 𝐶′(4,−3)

Q10:

Given that 𝑋(4,−4), 𝑌(8,−5), and 𝑍(5,−6), form a triangle, determine the images of its vertices after a clockwise rotation of 90∘ about the origin.

  • A𝑋′(−4,−4), 𝑌′(−5,−8), 𝑍′(6,5)
  • B𝑋′(4,4), 𝑌′(−5,−8), 𝑍′(−6,−5)
  • C𝑋′(−4,−4), 𝑌′(5,8), 𝑍′(−6,−5)
  • D𝑋′(−4,−4), 𝑌′(−5,−8), 𝑍′(−6,−5)
  • E𝑋′(4,4), 𝑌′(5,8), 𝑍′(6,5)

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