Note that PC=PC', for example, since they are the radii of the same circle.)Ī positive angle of rotation turns a figure counterclockwise (CCW),Īnd a negative angle of rotation turns the figure clockwise, (CW). Math Rotations Students learn that when a figure is turned to a new position, the transformation is called a rotation. For rotations of 90, 180, and 270 in either direction around the origin (0. A rotat ion does this by rotat ing an image a certain amount of degrees either clockwise or counterclockwise. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. (The dashed arcs in the diagram below represent the circles, with center P, through each of the triangle's vertices. A rotation is a type of rigid transformation, which means it changes the position or orientation of an image without changing its size or shape. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. A rotation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image.Īn object and its rotation are the same shape and size, but the figures may be positioned differently.ĭuring a rotation, every point is moved the exact same degree arc along the circleĭefined by the center of the rotation and the angle of rotation. Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. When working in the coordinate plane, the center of rotation should be stated, and not assumed to be at the origin. A rotation of θ degrees (notation R C,θ ) is a transformation which "turns" a figure about a fixed point, C, called the center of rotation.