Lesson Worksheet: Rotations about a Point Mathematics • 8th Grade

In this worksheet, we will practice rotating points, line segments, and shapes about given points.

Q1:

Which point represents point 𝐴 after a rotation of 𝑅(𝑀,20)?

  • APoint 𝐵
  • BPoint 𝐹
  • CPoint 𝐷
  • DPoint 𝐶
  • EPoint 𝐸

Q2:

If 𝐴𝐵 is rotated about 𝐴 with a 72 angle, which line segment represents its final position?

  • A𝐴𝐶
  • B𝐴𝐸
  • C𝐴𝐹
  • D𝐴𝐷

Q3:

If 𝐴𝐵 is rotated about 𝑀 with a 90 angle, which line segment represents its final position?

  • A𝐶𝐷
  • B𝐷𝐴
  • C𝐵𝐶

Q4:

When the green triangle 𝐴𝐵𝐶 is rotated 90 about 𝐴, which triangle is its new position?

  • A𝐴𝐻𝐼
  • B𝐴𝐷𝐸
  • C𝐴𝐹𝐺

Q5:

If the green triangle 𝐴𝐶𝐵 is rotated about point 𝑀 with an angle of 72, which triangle represents its final position?

  • A𝐺𝐻𝐼
  • B𝐼𝐽𝐴
  • C𝐵𝐷𝐸
  • D𝐸𝐹𝐺

Q6:

Where does a rotation through 180 about 𝑀 send the segment 𝐹𝐴?

  • A𝐶𝐷
  • B𝐴𝐵
  • C𝐷𝐸
  • D𝐸𝐹

Q7:

What is the image of 𝐶𝐷𝑀 after a 108 rotation?

  • A𝐴𝐵𝑀
  • B𝑃𝐴𝑀
  • C𝐹𝐺𝑀
  • D𝐸𝐹𝑀

Q8:

𝐴𝐵𝐶 is the image of 𝐴𝐵𝐶 by a counterclockwise rotation of 𝑥 about 𝐴. Find 𝑥.

Q9:

The following figure is of a regular polygon of 10 sides.

What is the final position of 𝐴𝐵 when the line segment is rotated 180 about 𝑀?

  • A𝐹𝐺
  • B𝐸𝐹
  • C𝐺𝐻
  • D𝐻𝐼
  • E𝐼𝐽

What is the final position of 𝐴𝐵 when the line segment is rotated 180 about 𝑀?

  • A𝐸𝐹
  • B𝐹𝐺
  • C𝐺𝐻
  • D𝐼𝐽
  • E𝐻𝐼

By comparing the results of the two previous questions, are rotations with 180 equivalent to rotations with 180 about a given point?

  • AYes
  • BNo

Q10:

Consider the octagon shape 𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻 with 𝑀 as its center.

What is the final position of 𝐴𝐵 when it is rotated 90?

  • A𝐶𝐷
  • B𝐸𝐹
  • C𝐺𝐻
  • DNone of the answers are correct.

What is the final position of 𝐴𝐵 when it is rotated 270?

  • A𝐺𝐻
  • B𝐸𝐹
  • C𝐶𝐷
  • DNone of the answers are correct.

Is there a difference between the two rotations?

  • ANo
  • BYes

Practice Means Progress

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