![]() ![]() 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 dashed arcs in the diagram below represent the circles, with center P, through each of the triangle's vertices. The final figure is exactly equal to the original. Clearly, P will be similarly situated on that side of OY which is. A congruence transformation is a moved figure that retains the same size, shape, angles, and side lengths of the original image. 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. Let P be a point whose coordinates are (x, y). Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. Translations are transformations that slide, or translate, a figure over a. Examples shown are reflect across the x-axis, reflect across the y-axis, reflect across the line y x. In the past, you investigated coordinate translations, reflections, and dilations. ![]() This video shows reflection over the x-axis, y-axis, x 2, y 2. To find a reflected image by measuring, you need to draw lines that are perpendicular to the reflection line, and measure the distances so that the distance. ![]() The following diagram shows how to reflect points and figures on the coordinate plane. Ordered pair rules reflect over the x-axis: (x, -y), y-axis: (-x, y), line y x: (y, x). For each of the figures points: - multiply the x-value by -1. When working in the coordinate plane, the center of rotation should be stated, and not assumed to be at the origin. Ordered pair rules reflect over the x-axis: (x, -y), y-axis: (-x, y), line y x: (y, x). 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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