Rotations: graph the image (Tutorial Only)

Learning Objectives Identify the center of rotation, angle of rotation, and direction for a given transformation. Apply the coordinate rules for 90°, 180°, and 270° rotations about the origin. Accurately graph the image of a single point after a specified rotation about the origin. Accurately graph the image of a polygon by rotating its vertices about the origin. Verify that a rotation is a rigid transformation by confirming that the image is congruent to the pre-image. Describe the specific rotation that maps a given pre-image to its image on the coordinate plane. Have you ever wondered how a video game character spins around or how a Ferris wheel moves in a perfect circle? 🎡 That's the magic of rotations! In this tutorial, you will learn how to perform rotations, a...

TermDefinitionExample RotationA transformation that turns a figure about a fixed point. Every point in the figure moves in a circular arc around this central point.A clock's hands rotate around the center of the clock face. Center of RotationThe fixed point around which a figure is rotated. In this tutorial, our center of rotation will always be the origin (0, 0).The point where the blades of a windmill connect is the center of rotation for the blades. Angle of RotationThe measure of the angle by which a figure is turned. It is typically measured in degrees.A 90° rotation is a quarter turn. A 180° rotation is a half turn. Pre-imageThe original figure before any transformation is applied.If we rotate triangle ABC, then triangle ABC is the pre-image. ImageThe new figure that results fr...

90° Counterclockwise Rotation (or 270° Clockwise) R_{90°, CCW}(x, y) = (-y, x) To rotate a point 90° counterclockwise about the origin, swap the x and y coordinates, and then negate the new x-coordinate. 180° Rotation (Clockwise or Counterclockwise) R_{180°}(x, y) = (-x, -y) To rotate a point 180° about the origin, simply negate both the x and y coordinates. The direction does not matter for a 180° rotation. 270° Counterclockwise Rotation (or 90° Clockwise) R_{270°, CCW}(x, y) = (y, -x) To rotate a point 270° counterclockwise about the origin, swap the x and y coordinates, and then negate the new y-coordinate.