Presentation on theme: "Goal: to rotate a figure around a central point"— Presentation transcript:
1Goal: to rotate a figure around a central point TransformationsGoal: to rotate a figure around a central point
2Transformations and rotations Transformation refers to any copy of a geometric figure, similar to copying and pasting on your computer.A Rotation is a type of transformation where the geometric figure is spun around a fixed point known as the “center of rotation”.Rotations can be made “clockwise” and “counterclockwise”.Common rotations are 45, 90, 180, and 270 degrees.Rotation A to A’ 90 degrees counter clockwise
3Rotation by 180° about the origin: R(origin, 180°)
4Graphing RotationsThe easiest way to think about rotations is to first think of a single coordinate rotation.1. Graph the point (1,2) on your paper.2. Rotate this point 90 degrees clockwise by first drawing a straight line to the “origin”.3. Secondly, draw a straight line from the origin down and to the right in order to form a right angle.4. Your second point should fall at (2,-1).
5180-degree rotation1. From the same point (1,2), draw a straight line through the origin.2. The point that your line hits that is equidistance from (1,2) is your 180-degree clockwise rotation.3. Your second point should fall at (-1,-2)
6270-degree rotation1. Start from (1,2), draw a straight line through the origin until you hit (-1,-2).2. This is 180 degrees from the last example.3. We must add 90 degrees to this.4. Draw another line from the origin up and to the left to make a 90-degree angle between (-1,-2), the origin, and a last point.5. This point should fall on (-2,1).
7RULE: A rotated object’s vertices will form an angle with its original object’s vertices equal to the degree measure of the rotation.The above rotation shows 90-degree angles between all rotated vertices.
8Example 2: 180-degree rotation All of the vertices of the triangle on the left are rotated 180 degrees through the center of reflection.