A rigid transformation that turns every point of a figure by a fixed angle around a fixed center of rotation.
Like a Ferris wheel turning around its center hub—every seat traces a circle, staying the same distance from the axle while sweeping through the same angle.
Showing a random 20 of 50 problems.
Example 1
hard
The point (6,2) is rotated 90° CW about an unknown center and lands at (2,−2). Find the center.P(6, 2) rotated 90° CW lands at P'(2, −2) — find the center C
Example 2
hard
Find the center of rotation for the rotation that sends A(1,0) to A′(0,1) and B(2,0) to B′(0,2).Find the center of rotation that sends A→A' and B→B'
Example 3
easy
What is the image of point (0,5) after a 180° rotation about the origin?Rotate (0, 5) by 180° about the origin
Example 4
challenge
A regular hexagon is rotated about its center. List all rotation angles (between 0∘ and 360∘) that map it onto itself.
Example 5
easy
Rotate (2,3) by 180∘ about the origin.Rotate (2, 3) by 180° about the origin
Example 6
medium
Triangle A(2,1), B(5,1), C(5,3) is rotated 90° CCW about the origin. Find the image vertices.Triangle ABC rotated 90° CCW about the origin
Example 7
medium
Rotate the segment from A(0,0) to B(3,4) by 90° CCW about A. Find B′.Rotate segment AB by 90° CCW about A(0, 0)
Example 8
hard
Rotate the point (1,0) by 45° counterclockwise about the origin. Give exact coordinates.
Example 9
medium
Rotate the point (4,2) by 270∘ counterclockwise about the origin.Rotate (4, 2) by 270° CCW about the origin
Example 10
easy
Rotate the point (−3,5) by 180° about the origin.Rotate (-3, 5) by 180° about the origin
Example 11
hard
What single rotation about the origin equals the composition of a 250° CCW rotation followed by a 190° CCW rotation about the origin?
Example 12
easy
A 90∘ clockwise rotation is the same as how many degrees counterclockwise?
Example 13
medium
Rotate the point B(4,0) by 60° counterclockwise about the origin. Give exact coordinates.
Example 14
easy
Rotate the point A(3,2) by 90° counterclockwise about the origin. Where does A end up?Rotate A(3, 2) by 90° CCW about the origin
Example 15
challenge
Explain why a rotation (other than 0∘ or 360∘) has exactly one fixed point.
Example 16
medium
Rotate the point (2,0) by 30° counterclockwise about the origin. Give exact coordinates.
Example 17
easy
Rotate the point (4,1) by 90° counterclockwise about the origin.Rotate (4, 1) by 90° CCW about the origin
Example 18
easy
Does a rotation change a figure's size?
Example 19
easy
After rotating a figure 360∘, where does it end up?
Example 20
medium
A rotation of 90∘ is applied twice. What single rotation is equivalent?