Lesson Worksheet: Rotations on the Coordinate Plane Mathematics • 8th Grade

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In this worksheet, we will practice finding the vertices of a shape after it undergoes a rotation of 90, 180, or 270 degrees about the origin clockwise and counterclockwise.

Q1:

Determine the images of the vertices of triangle 𝐴𝐡𝐢 after a clockwise rotation of 90∘ about the origin.

  • A𝐴′(βˆ’4,8), 𝐡′(βˆ’3,3), 𝐢′(7,βˆ’3)
  • B𝐴′(4,βˆ’8), 𝐡′(βˆ’3,3), 𝐢′(βˆ’7,3)
  • C𝐴′(4,βˆ’8), 𝐡′(3,βˆ’3), 𝐢′(7,βˆ’3)
  • D𝐴′(βˆ’4,8), 𝐡′(3,βˆ’3), 𝐢′(βˆ’7,3)
  • E𝐴′(βˆ’4,8), 𝐡′(βˆ’3,3), 𝐢′(βˆ’7,3)

Q2:

Given that 𝑋(4,βˆ’2), π‘Œ(8,βˆ’3), and 𝑍(5,βˆ’8) form a triangle, determine the images of its vertices after a clock wise rotation of 180∘ about the origin.

  • A𝑋′(2,βˆ’4), π‘Œβ€²(3,βˆ’8), 𝑍′(8,βˆ’5)
  • B𝑋′(βˆ’4,2), π‘Œβ€²(3,βˆ’8), 𝑍′(βˆ’5,8)
  • C𝑋′(2,βˆ’4), π‘Œβ€²(βˆ’8,3), 𝑍′(βˆ’5,8)
  • D𝑋′(βˆ’4,2), π‘Œβ€²(βˆ’8,3), 𝑍′(8,βˆ’5)
  • E𝑋′(βˆ’4,2), π‘Œβ€²(βˆ’8,3), 𝑍′(βˆ’5,8)

Q3:

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

  • A(βˆ’3,βˆ’14)
  • B(βˆ’14,3)
  • C(3,14)
  • D(βˆ’14,βˆ’3)

Q4:

What is the image of 𝐴𝐡𝐢𝐷 under the transformation (π‘₯,𝑦)β†’(βˆ’π‘¦,π‘₯)?

  • A𝐴′(4,βˆ’3), 𝐡′(5,βˆ’3), 𝐢′(5,βˆ’4), 𝐷′(4,βˆ’5)
  • B𝐴′(βˆ’4,3), 𝐡′(βˆ’5,3), 𝐢′(βˆ’5,4), 𝐷′(βˆ’4,5)
  • C𝐴′(4,5), 𝐡′(5,5), 𝐢′(5,6), 𝐷′(4,7)
  • D𝐴′(4,0), 𝐡′(5,0), 𝐢′(5,1), 𝐷′(4,2)
  • E𝐴′(βˆ’3,4), 𝐡′(βˆ’3,5), 𝐢′(βˆ’4,5), 𝐷′(βˆ’5,4)

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(βˆ’1,2),(βˆ’2,3), and (βˆ’4,2)
  • B(1,2),(2,3), and (2,βˆ’4)
  • C(βˆ’2,1),(βˆ’2,3), and (4,βˆ’2)
  • D(2,βˆ’1),(3,βˆ’2), and (2,βˆ’4)
  • E(βˆ’1,2),(2,3), and (2,βˆ’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(βˆ’2,1),(βˆ’2,4), and (βˆ’5,2)
  • D(1,βˆ’2),(4,βˆ’2), and (2,βˆ’5)
  • E(2,βˆ’1),(4,βˆ’2), and (2,βˆ’5)

Q7:

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

  • A𝐴′(8,βˆ’7), 𝐡′(3,βˆ’7), 𝐢′(4,βˆ’3)
  • B𝐴′(βˆ’7,8), 𝐡′(βˆ’7,3), 𝐢′(βˆ’3,4)
  • C𝐴′(8,βˆ’7), 𝐡′(βˆ’7,3), 𝐢′(4,βˆ’3)
  • D𝐴′(8,βˆ’7), 𝐡′(3,βˆ’7), 𝐢′(βˆ’3,4)
  • E𝐴′(βˆ’7,8), 𝐡′(3,βˆ’7), 𝐢′(4,βˆ’3)

Q8:

Given that 𝑋(4,βˆ’4), π‘Œ(8,βˆ’5), and 𝑍(5,βˆ’6), form a triangle, determine the images of its vertices after a clockwise rotation of 90∘ about the origin.

  • A𝑋′(βˆ’4,βˆ’4), π‘Œβ€²(βˆ’5,βˆ’8), 𝑍′(6,5)
  • B𝑋′(4,4), π‘Œβ€²(βˆ’5,βˆ’8), 𝑍′(βˆ’6,βˆ’5)
  • C𝑋′(βˆ’4,βˆ’4), π‘Œβ€²(5,8), 𝑍′(βˆ’6,βˆ’5)
  • D𝑋′(βˆ’4,βˆ’4), π‘Œβ€²(βˆ’5,βˆ’8), 𝑍′(βˆ’6,βˆ’5)
  • E𝑋′(4,4), π‘Œβ€²(5,8), 𝑍′(6,5)

Q9:

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

  • A𝐴′(βˆ’3,7), 𝐡′(3,βˆ’4), 𝐢′(βˆ’5,6)
  • B𝐴′(βˆ’3,7), 𝐡′(βˆ’4,3), 𝐢′(6,βˆ’5)
  • C𝐴′(7,βˆ’3), 𝐡′(βˆ’4,3), 𝐢′(βˆ’5,6)
  • D𝐴′(7,βˆ’3), 𝐡′(3,βˆ’4), 𝐢′(6,βˆ’5)
  • E𝐴′(βˆ’3,7), 𝐡′(βˆ’4,3), 𝐢′(βˆ’5,6)

Q10:

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

This lesson includes 39 additional questions and 125 additional question variations for subscribers.

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