Rotations: graph the image

Learning Objectives Identify and describe a rotation as a type of transformation. Determine the center and angle of rotation for a given transformation. Apply the coordinate rules for 90°, 180°, and 270° rotations about the origin. Calculate the coordinates of a rotated image given the pre-image coordinates. Accurately graph the image of a figure after a rotation on the coordinate plane. Distinguish rotations from other transformations like translations and reflections. Have you ever wondered how a Ferris wheel spins or how a clock's hands move? 🎡 These are all examples of rotations in action! In this lesson, we'll explore rotations, a fundamental type of geometric transformation. You'll learn how to spin shapes around a fixed point on a coordinate plane an...

TermDefinitionExample TransformationA change in the position, size, or orientation of a geometric figure.Moving a triangle from one spot on a graph to another. RotationA transformation that turns a figure about a fixed point called the center of rotation.Spinning a square 90 degrees around its center. Pre-imageThe original figure before a transformation is applied.If you start with triangle ABC, it is the pre-image. ImageThe new figure formed after a transformation has been applied to the pre-image. It is often denoted with prime notation (e.g., A').After rotating triangle ABC, the new triangle A'B'C' is the image. Center of RotationThe fixed point around which a figure is rotated. For Grade 8, this is typically the origin (0,0).When a clock's hands move, the cent...

Rotation 90° Counter-Clockwise (CCW) about the Origin $(x, y) \rightarrow (-y, x)$ To rotate a point 90 degrees counter-clockwise around the origin, swap the x and y coordinates, and then change the sign of the new x-coordinate (which was the original y-coordinate). Rotation 180° about the Origin $(x, y) \rightarrow (-x, -y)$ To rotate a point 180 degrees around the origin (either clockwise or counter-clockwise, as the result is the same), change the signs of both the x and y coordinates. Rotation 270° Counter-Clockwise (CCW) about the Origin $(x, y) \rightarrow (y, -x)$ To rotate a point 270 degrees counter-clockwise around the origin, swap the x and y coordinates, and then change the sign of the new y-coordinate (which was the original x-coordinate).