Rotations: find the coordinates

Learning Objectives Define rotation and its key properties: center, angle, and direction. Apply the coordinate rule for a 90° counter-clockwise rotation about the origin. Apply the coordinate rule for a 90° clockwise rotation about the origin. Apply the coordinate rule for a 180° rotation about the origin. Determine the coordinates of the vertices of a polygon after a rotation about the origin. Differentiate between the rules for clockwise and counter-clockwise rotations. Verify that rotation is a rigid motion that preserves side lengths and angle measures. Ever wondered how a character in a video game or a Ferris wheel car turns so perfectly? 🎡 That movement is a mathematical rotation, and you can calculate its exact position! This tutorial will teach you the precise ru...

TermDefinitionExample RotationA transformation that turns a figure about a fixed point. Every point in the figure moves in a circular arc.A spinner on a board game rotates around its center pin. Center of RotationThe fixed point around which a figure is turned. In this lesson, the center of rotation will always be the origin (0, 0).The center of a clock face where the hands are attached. Angle of RotationThe measure of the angle by which a figure is turned. Common angles are 90°, 180°, and 270°.A 90° rotation is a quarter turn. A 180° rotation is a half turn. Direction of RotationThe direction of the turn, which can be clockwise (like the hands of a clock) or counter-clockwise (the opposite direction). By convention, a positive angle means counter-clockwise.Turning a screw 'righty-ti...

90° Counter-clockwise Rotation (or 270° Clockwise) R_{90°, O}(x, y) = (-y, x) To rotate a point 90° counter-clockwise about the origin, swap the x and y coordinates, then negate the new x-coordinate. 180° Rotation (Clockwise or Counter-clockwise) R_{180°, O}(x, y) = (-x, -y) To rotate a point 180° about the origin, simply negate both the x and y coordinates. The order of the coordinates does not change. 90° Clockwise Rotation (or 270° Counter-clockwise) R_{-90°, O}(x, y) = (y, -x) To rotate a point 90° clockwise about the origin, swap the x and y coordinates, then negate the new y-coordinate.