Rotate polygons about a point (Tutorial Only)

Learning Objectives Define rotation and identify its key properties: center, angle, and direction. Apply coordinate rules to rotate polygons 90°, 180°, and 270° counterclockwise about the origin. Perform a rotation of a polygon about a point other than the origin using the translate-rotate-translate method. Graphically rotate a polygon using tools like a compass and protractor. Determine the center and angle of rotation given a pre-image and its rotated image. Prove that rotation is a rigid motion (isometry) by showing it preserves side lengths and angle measures. Have you ever wondered how a Ferris wheel spins perfectly around its center, or how animators make a character turn? 🎡 That's the magic of rotation in action! In this tutorial, we will explore rotation, a fu...

TermDefinitionExample RotationA transformation that turns a figure about a fixed point. Every point in the figure moves in a circular arc around this fixed point.Turning a square 90 degrees counterclockwise around its center point. Center of RotationThe single fixed point around which a figure is turned. This is the only point that does not move during the rotation.The center of a clock face, where the hands are attached. Angle of RotationThe measure of the angle by which a figure is turned. It is formed by a point on the pre-image, the center of rotation, and the corresponding point on the image.A 180° rotation flips a figure upside down. Direction of RotationThe orientation of the turn. Unless specified otherwise, rotations are counterclockwise. A positive angle indicates a counterclock...

90° Counterclockwise Rotation about the Origin R_{90°, O}(x, y) = (-y, x) To rotate a point 90° counterclockwise around the origin (0,0), switch the x and y coordinates and negate the new x-coordinate. 180° Rotation about the Origin R_{180°, O}(x, y) = (-x, -y) To rotate a point 180° around the origin (0,0), negate both the x and y coordinates. The direction (clockwise or counterclockwise) does not matter for a 180° rotation. 270° Counterclockwise Rotation about the Origin R_{270°, O}(x, y) = (y, -x) To rotate a point 270° counterclockwise around the origin (0,0), switch the x and y coordinates and negate the new y-coordinate. This is equivalent to a 90° clockwise rotation.