A rotation is a transformation in which every point is rotated the same angle measure around a fixed point. The fixed point is called the center of rotation.
The ray drawn from the center of rotation to a point and the ray drawn from the center of rotation to the point’s image form an angle called the angle of rotation.
Rotations can be clockwise ( ) or counterclockwise ( ).
Let’s take a look at rotations in the coordinate plane.
Example 1: Rotate 180 clockwise about the origin (0, 0). Give the coordinates of _______ _______
Would the coordinates of and be different if we had rotated counterclockwise instead? NO
Rotations around the origin can be made very easily by simply rotating your paper the required angle measure. Note: The horizontal axis is always the x-axis and the vertical axis is always the y-axis.
Example 2: Rotate 90 clockwise about the origin. Give the coordinates of ________ ________
Example 3: Rotate 90 counterclockwise about the origin. Give the coordinates of ________ ________ A B
For rotations of 90 0 around a point other than the origin, we must work with the slopes of the rays forming the angle of rotation. Remember: If two rays are perpendicular then their slopes are opposite reciprocals.
Example 4: Rotate 90 clockwise about the point (–1, 3).
Example 4: Rotate 90 counterclockwise about the point (–1, 3).
Example 6: Rotate 90 0 counterclockwise around the point (3, 0)
A figure has rotational symmetry if it can be rotated through an angle of less than 360 and match up with itself exactly.
Example 7: State the rotational symmetries of a square regular pentagon
Example 8: Name two capital letters that have 180 rotational symmetry.