Rotations: graph the image (Tutorial Only)

Learning Objectives Define rotation, center of rotation, and angle of rotation. Identify the direction of rotation (clockwise or counter-clockwise). Apply the rules for 90-degree and 180-degree rotations around the origin. Find the coordinates of a rotated point or vertex. Accurately graph the image of a point or a simple shape after a rotation around the origin. Distinguish between a pre-image and its rotated image on a coordinate plane. Have you ever spun a toy top or watched the hands of a clock move? 🕰️ That's a rotation! How can we show these turns on a graph? In this lesson, you'll learn all about rotations, which are a type of transformation that turns a figure around a fixed point. We'll discover how to find the new position of points and shapes after...

TermDefinitionExample RotationA transformation that turns a figure around a fixed point called the center of rotation.Spinning a pinwheel is an example of a rotation. Center of RotationThe fixed point around which a figure is rotated. In this lesson, we will mostly use the origin (0,0) as our center.If you spin a pizza on your finger, your finger is the center of rotation. Angle of RotationThe amount of turn, measured in degrees, that a figure rotates. Common angles are 90°, 180°, and 270°.Turning a doorknob a quarter turn is a 90° rotation. ClockwiseThe direction of rotation that is the same as the way the hands on a clock move (to the right).Turning a screw to tighten it often involves a clockwise rotation. Counter-ClockwiseThe direction of rotation that is opposite to the way the hands...

90° Clockwise Rotation around the Origin $(x, y) \rightarrow (y, -x)$ To rotate a point 90 degrees clockwise around the origin (0,0): first, swap the x and y coordinates. Then, change the sign of the new y-coordinate (the original x-coordinate). 90° Counter-Clockwise Rotation around the Origin $(x, y) \rightarrow (-y, x)$ To rotate a point 90 degrees counter-clockwise around the origin (0,0): first, swap the x and y coordinates. Then, change the sign of the new x-coordinate (the original y-coordinate). 180° Rotation around the Origin (Clockwise or Counter-Clockwise) $(x, y) \rightarrow (-x, -y)$ To rotate a point 180 degrees around the origin (0,0) (the direction doesn't matter for 180°): simply change the sign of both the x-coordinate and the y-coordinate.