Rotations: graph the image (Tutorial Only)

Learning Objectives Define rotation, center of rotation, angle of rotation, and direction of rotation. Identify the pre-image and image of a figure after a rotation. Apply coordinate rules for 90°, 180°, and 270° rotations about the origin. Graph the image of a point or polygon after a given rotation on a coordinate plane. Distinguish between clockwise and counter-clockwise rotations. Accurately label the vertices of the rotated image using prime notation. 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 tutorial, you'll learn all about rotations, a type of transformation that turns a figure around a fixed point. We'll explore how to use coordinate rules to find the new po...

TermDefinitionExample RotationA transformation that turns a figure around a fixed point, called the center of rotation, without changing its size or shape.Turning a square 90 degrees around its center point. Center of RotationThe fixed point around which a figure is rotated. In this lesson, we will primarily focus on rotations around the origin (0,0) of the coordinate plane.If you spin a pinwheel, the pin holding it in place is the center of rotation. Angle of RotationThe number of degrees a figure is turned around the center of rotation. Common angles are 90°, 180°, and 270°.A clock's minute hand moves 360° in one hour, or 90° every 15 minutes. Direction of RotationThe way a figure is turned. It can be either clockwise (CW), like the hands of a clock, or counter-clockwise (CCW), the...

Rotation of 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 of 180° about the Origin (CCW or CW) $(x, y) \rightarrow (-x, -y)$ To rotate a point 180 degrees around the origin (either clockwise or counter-clockwise, as the result is the same), change the sign of both the x and y coordinates. Rotation of 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-coordin...