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.

Q1:

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)

Q2:

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

Q3:

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

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

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)

Q6:

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)

Q7:

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)

Q8:

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)

Q9:

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

Q10:

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.

Practice Means Progress

Download the Nagwa Practice app to access 39 additional questions for this lesson!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.