Rotations: find the coordinates

Learning Objectives Identify the center and angle of rotation for a given transformation. Apply the coordinate rules for 90-degree counter-clockwise rotations around the origin. Apply the coordinate rules for 180-degree rotations around the origin. Apply the coordinate rules for 270-degree counter-clockwise rotations around the origin. Determine the new coordinates of a point or a polygon after a rotation around the origin. Distinguish between clockwise and counter-clockwise rotations and their effects on coordinates. Have you ever spun a toy top or watched the hands of a clock move? 🕰️ These are everyday examples of rotations! In this lesson, we'll explore how to mathematically describe these 'spins' on the coordinate plane. You'll learn specific rules...

TermDefinitionExample RotationA transformation that turns a figure about a fixed point called the center of rotation.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 focus on rotations around the origin (0,0).If you spin a pizza on a tray, the center of the pizza is the center of rotation. Angle of RotationThe number of degrees a figure is rotated. Common angles are 90°, 180°, and 270°.A clock's minute hand rotates 360 degrees in one hour, or 90 degrees every 15 minutes. Direction of RotationThe way a figure turns: either clockwise (CW), like the hands of a clock, or counter-clockwise (CCW), the opposite direction.Turning a doorknob clockwise to open a door. Pre-imageThe original figure be...

Rotation by 90° Counter-Clockwise (CCW) around 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 by 180° around the Origin $(x, y) \rightarrow (-x, -y)$ To rotate a point 180 degrees around the origin (either clockwise or counter-clockwise), change the signs of both the x and y coordinates. Rotation by 270° Counter-Clockwise (CCW) around 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). This is equivalent to a 90° c...