Linear Algebra

1. Linear Algebra Thursday, august 14

2. Learning Target I will understand what is meant by turn or rotational symmetry and how each point in a figure is related to its image under transformation by rotation.

3. Rotational Symmetry • Rotational symmetry: A figure or design has rotational symmetry if it can be rotated less than a full turn about a point to a position in which it looks the same as the original. The design below has rotational symmetry with its center as the center of rotation and a 60o angle of rotation. This means that it can be rotated 60o, or any multiple of 60o, about its center point to produce an image that matches exactly with the original.

4. Rotational Symmetry • Rotation: A transformation that turns a figure counterclockwise about a point. Polygon A’B’C’D’ below is the image of polygon ABCD under a 60o rotation about point P. If you drew a segment from a point on polygon ABCD to point P and another segment from the point’s image to point P, the segments would be the same length and they would form a 60o angle The line segment D’ to P and D to P are of equal length. The angle formed is 60o

5. Rotational Symmetry • Center of rotation: A fixed point about which a figure rotates. Center of rotation

6. Rotational Symmetry • Angle of rotation: The number of degrees that a figure rotates. In the example below the angle of rotation is 90o. ABC is rotated counterclockwise 90o about point P to result in image A’B’C’.