# Worksheet: Rotations on Coordinate Plane

In this worksheet, we will practice rotating a shape through 90, 180, and 270 degrees about the origin and investigating what happens to the coordinates as a result.

**Q2: **

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 , ,

**Q3: **

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

- A
- B
- C
- D

**Q4: **

What type of transformation is the following?

- Atranslation
- Breflection
- Crotation

**Q6: **

Which transformation can turn the letter d into p?

- Atranslation
- Breflection
- Crotation

**Q7: **

Which transformation can turn the letter Z into N?

- Atranslation
- Breflection
- Crotation

**Q8: **

Which of the following represents a rotation of the shaded figure?

- A
- B
- C
- D

**Q9: **

A triangle has its vertices at the points (2, 1), (3, 2) and (2, 4). The triangle is rotated counterclockwise about the origin. At which of the following coordinates will the image have its vertices?

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

**Q10: **

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

**Q11: **

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

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

**Q12: **

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 , ,

**Q13: **

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

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

**Q14: **

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

**Q15: **

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 centre
- Ba circle with radius two and centre
- Ca circle with radius three and centre
- Da circle with radius three and centre
- Ea circle with radius three and centre

**Q16: **

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
- Bless than
- Cgreater than

**Q17: **

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

- A a rotation of clockwise about
- B a rotation of clockwise about
- C a rotation of clockwise about
- D a rotation of counterclockwise about
- Ea rotation of counterclockwise about

**Q18: **

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

**Q19: **

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

- A
- B
- C
- D
- E

**Q20: **

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

- A
- B
- C
- D
- E

**Q21: **

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

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

**Q22: **

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?

- A yes
- B no

**Q23: **

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

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

**Q24: **

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?

- A true
- B false

**Q25: **

is rotated clockwise about the origin. Is the length of the image resulting from this transformation greater than, less than, or the same as the length of ?

- Aless than
- Bgreater than
- Cthe same