Rotation

Rotation is a circular motion around the particular axis of rotation or point of rotation. In general, rotation can be done in two common directions, clockwise and anti-clockwise or counter-clockwise direction.

To rotate an object around a fixed point:
1. Determine if the movement will be clockwise (negative) or counter-clockwise (positive).
2. Starting at the fixed point the object will be rotating around, find the two lines that connect to that point.
3. Choose one of the lines to rotate first. Move that line in the clockwise or counter-clockwise direction until it has completely rotated around the point in the number of degrees required. Draw the line (with the same length) in the new location.
4. Choose the second line to rotate next. Move that line in the clockwise or counter-clockwise direction until it has completely rotated around the point in the number of degrees required. Draw the line (with the same length) in the new location.
5. Draw the rest of the lines needed to complete the shape.

To rotate an object about the origin:
A rotation about the origin, is a rotation that has a center of rotation at the origin (0,0).

Graph the image given, rotated around the origin 180 degrees.

Find the coordinates for all of the vertices. A(1, -2), B(4, -2), C(4, -4), and D(0, -4). For a 180 degree rotation around the origin, use the rule (x, y) → (-x, -y). This means to take the opposite of both the x and y coordinate values in the preimage to get the coordinates of the image.
A'(-1, 2), B'(-4, 2), C'(-4, 4), and D'(0, 4).