Rotations: find the coordinates

Learning Objectives Define and identify key components of a rotation, including the center and angle of rotation. Distinguish between clockwise and counter-clockwise rotations. Apply rotation rules to find the coordinates of a single point after a 90, 180, or 270-degree rotation around the origin. Determine the coordinates of the vertices of a polygon after a rotation around the origin. Accurately graph the image of a point or polygon after a rotation on the coordinate plane. Identify and correct common errors made when performing rotations and finding new coordinates. Ever wondered how a Ferris wheel spins 🎡 or how a clock's hands move? These are all examples of rotations! Today, we'll learn how to describe these turns mathematically on a coordinate plane. In th...

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 Grade 8, we typically focus on the origin (0,0).When spinning a pinwheel, the pin holding it in place 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 moves 360° in one hour, or 90° in 15 minutes. Clockwise Rotation (CW)A rotation in the same direction as the hands of a clock.Turning a screw to tighten it is often a clockwise rotation. Counter-Clockwise Rotation (CCW)A rotation in the opposite direction of the hands of a clock.Turning a doorknob to op...

Rotation 90° Counter-Clockwise (CCW) around the Origin $(x, y) \to (-y, x)$ 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° around the Origin $(x, y) \to (-x, -y)$ To rotate a point 180 degrees around the origin (either clockwise or counter-clockwise, as it results in the same image), change the signs of both the x and y coordinates. Rotation 270° Counter-Clockwise (CCW) around the Origin $(x, y) \to (y, -x)$ 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). Note: This is equivalent to a...