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). The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function. (The dashed arcs in the diagram below represent the circles, with center P, through each of the triangle's vertices. The original object is called the pre-image, and the reflection is called the image. Understand that there are an infinite number of fixed points with a reflection, but all fixed. Describe where the general rule is derived from. Use an algebraic rule to show the reflection of a figure over an axis or the line yx. To perform a geometry rotation, we first need to know the point of rotation, the angle of rotation, and a direction (either clockwise or counterclockwise). A reflection can be thought of as folding or 'flipping' an object over the line of reflection. Perform a reflection on a coordinate plane by reflecting points over any given line (not just an axis or yx). The orientation of the image also stays the same, unlike reflections. reflection: when a ray of light bounces off a reflective surface and returns into the medium from which it originated. 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. Geometry Rotation A rotation is an isometric transformation: the original figure and the image are congruent. A positive degree rotation runs counter clockwise and a negative degree rotation runs clockwise. Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. What are Rotations Rotations are a type of transformation in geometry where we take a point, line, or shape and rotate it clockwise or counterclockwise, usually by 90º,180º, 270º, -90º, -180º, or -270º. 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.
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