The terms rotation, reflection, translation, and dilation refer to basic geometric transformations that describe how shapes and figures can be manipulated in a plane. Here’s a brief explanation of each:
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Rotation: This transformation involves turning a figure around a fixed point, called the center of rotation. The amount of rotation is specified in degrees. For example, rotating a triangle 90 degrees clockwise around a point means turning every point in the triangle 90 degrees around that point.
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Reflection: Reflection is the transformation that produces a mirror image of a figure across a specific line known as the line of reflection. Points on the figure are mapped to points on the opposite side of the line at an equal distance.
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Translation: Translation involves sliding a figure from one position to another without altering its shape, size, or orientation. It is defined by a vector that indicates the direction and distance the figure is to be moved.
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Dilation: Dilation is a transformation that changes the size of a figure but keeps its shape the same. It involves scaling the figure by a certain factor, known as the scale factor. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.
These transformations can be applied individually or in combination to create more complex changes to geometric figures. They're fundamental concepts in geometry and are often used in various applications, including computer graphics, engineering, and various fields of science.