Rotations: graph the image

Learning Objectives Define key terms related to rotations, such as 'center of rotation' and 'angle of rotation'. Identify the direction of rotation as either clockwise or counter-clockwise. Apply rules for rotating points 90 degrees clockwise, 90 degrees counter-clockwise, and 180 degrees around the origin. Calculate the new coordinates of a point after a specified rotation around the origin. Accurately plot the original point (pre-image) and the rotated point (image) on a coordinate plane. Graph the image of a simple shape (like a triangle or square) after a rotation around the origin. Have you ever spun a toy top or watched the hands of a clock move? 🕰️ That's a rotation! What happens to an object when it spins or turns? In this lesson, we'll...

TermDefinitionExample RotationA transformation that turns a shape around a fixed point without changing its size or shape.Turning a square on a piece of paper around one of its corners. Center of RotationThe fixed point around which a shape turns during a rotation. For Grade 5, this is usually the origin (0,0).The center of a clock is the center of rotation for its hands. Angle of RotationThe amount, in degrees, that a shape is turned. Common angles are 90°, 180°, and 270°.A clock's minute hand moves 360° in one hour, or 90° in 15 minutes. ClockwiseThe direction in which the hands of a clock move (to the right, then down, then left, then up).Turning a screw to tighten it is often a clockwise rotation. Counter-ClockwiseThe opposite direction of clockwise (to the left, then down, then...

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. Second, change the sign of the *new* y-coordinate (which was your 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. Second, change the sign of the *new* x-coordinate (which was your original y-coordinate). 180° Rotation around the Origin $(x, y) \rightarrow (-x, -y)$ To rotate a point 180 degrees around the origin (0,0) (it's the same whether clockwise or counter-clockwise!): Simply change the signs of *both* the x and y coordinates.