# Worksheet: Rotations on the Coordinate Plane

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.

**Q2: **

Given that , , and form a triangle, determine the images of its vertices after a clock wise rotation of about the origin.

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q3: **

What is the image of the point after a rotation about the origin through an angle of ?

- A
- B
- C
- D

**Q6: **

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

- A , and
- B , and
- C , and
- D , and
- E , and

**Q7: **

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

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q8: **

Given that , , and , form a triangle, determine the images of its vertices after a clockwise rotation of about the origin.

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q9: **

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

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q10: **

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

- A clockwise around the origin
- B counterclockwise around the origin
- C clockwise or counterclockwise around the origin

**Q11: **

The point is rotated about the origin by degrees. On which of the given figures will the image of lie?

- Aa circle with radius three and center
- Ba circle with radius three and center
- Ca circle with radius three and center
- Da circle with radius three and center
- Ea circle with radius two and center

**Q12: **

Two points and have coordinates and respectively. is rotated counterclockwise to .

Determine the coordinates of and .

- A ,
- B ,
- C ,
- D ,
- E ,

Is the length of greater than, less than, or equal to the length of ?

- Aequal to
- Bgreater than
- Cless than

**Q13: **

Describe the single transformation that would map triangle onto triangle in the given figure.

- Aa rotation of counterclockwise about
- Ba rotation of clockwise about
- Ca rotation of clockwise about
- Da rotation of clockwise about
- Ea rotation of counterclockwise about

**Q14: **

A triangle has vertices at the points seen in the figure. Rotate the triangle counterclockwise about the origin, and determine the coordinates of the image.

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q15: **

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

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q16: **

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

- A
- B
- C
- D
- E

**Q17: **

and are parallel. Both have been rotated clockwise about the point to and respectively. What do you notice about and ?

- AThey are parallel.
- BThey are intersecting.
- CThey are perpendicular.

**Q18: **

In the given figure, a rotation of counterclockwise about the point would map triangle to triangle . Does it follow that the two triangles are congruent?

- Ano
- Byes

**Q19: **

A rotation about takes to and to . What is the angle of rotation? If , what is ?

- A , 90
- B , 45
- C , 45
- D , 45

**Q20: **

In the given figure, if is the midpoint of , then can be rotated about to . Hence, and must be congruent. Is this statement true or false?

- Afalse
- Btrue

**Q21: **

The vertices of are , , and . Determine the vertices of , the image of after a rotation through about the origin.

- A , ,
- B , ,
- C , ,
- D , ,

**Q22: **

Isabella went on a hike in the woods. She was walking southwest along a trail. When she got to a fork in the trail, she started walking southeast. Fully describe the rotation she made at the fork in the trail.

- ARotation by counterclockwise
- BRotation by counterclockwise
- CRotation by clockwise
- DRotation by clockwise
- ERotation by clockwise

**Q23: **

The point is the image of the point after a anticlockwise rotation of about the origin. Find and .

- A ,
- B ,
- C ,
- D ,

**Q24: **

In the figure, has been rotated about the origin by . Is the image a point, a line segment, or a line?

- Aa point
- Ba line segment
- Ca line

**Q25: **

Points and have coordinates and respectively.

What is the length of ?

A rotation of clockwise about the origin maps the points and to the points and respectively. What are the coordinates of and ?

- A ,
- B ,
- C ,
- D ,
- E ,

What is the length of ?

Hence, does the length of decrease, increase, or stay the same as a result of this rotation?

- AIt decreases.
- BIt stays the same.
- CIt increases.