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

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.


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)


If the image of the point (π‘₯,𝑦) by rotation about the origin point with an angle measuring 270∘ is (π‘Ž,𝑏), find the value of π‘Ž+𝑦 and 𝑏+π‘₯.

  • Aπ‘Ž+𝑦=0, 𝑏+π‘₯=2π‘₯
  • Bπ‘Ž+𝑦=0, 𝑏+π‘₯=0
  • Cπ‘Ž+𝑦=0, 𝑏+π‘₯=2𝑦
  • Dπ‘Ž+𝑦=2𝑦, 𝑏+π‘₯=0


Which of the following is equivalent to a 25∘ rotation about the origin?

  • AA βˆ’25∘ rotation about the origin
  • BA 25∘ rotation about the point (1,1)
  • CA βˆ’155∘ rotation about the origin
  • DA βˆ’335∘ rotation about the origin
  • EA 335∘ rotation about the origin


If triangle 𝐴𝐡𝐢 is rotated by 𝑅(𝑂,90)∘, which triangle would represent its final position?

  • A
  • B
  • C
  • D
  • E


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)


If we rotated the line segment 𝐴𝐡 about the origin by an angle of 90∘, what would its final position be?

  • A𝐴′(βˆ’1,βˆ’2), 𝐡′(βˆ’3,βˆ’4)
  • B𝐴′(1,βˆ’2), 𝐡′(3,βˆ’4)
  • C𝐴′(βˆ’2,1), 𝐡′(βˆ’4,3)
  • D𝐴′(2,βˆ’1), 𝐡′(4,βˆ’3)
  • E𝐴′(βˆ’1,2), 𝐡′(βˆ’3,4)


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)


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)


In the figure, 𝐴𝐡 has been rotated 90∘ counterclockwise about the origin. Is the length of the image 𝐴′𝐡′ resulting from this transformation greater than, less than, or the same as the length of 𝐴𝐡?

  • Agreater than
  • Bthe same
  • Cless than


The square in the figure has been rotated 90∘ counterclockwise about the point 𝐸. Do the measures of the square’s angles decrease, increase, or stay the same as a result of this transformation?

  • AThey increase.
  • BThey stay the same.
  • CThey decrease.

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