# 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.

Q1:

Determine the images of the vertices of triangle after a clockwise rotation of about the origin. • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

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

Q4:

What is the image of under the transformation ? • A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Q5:

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

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 about the origin by 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:

Emma 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.