![]() ![]() Dilations, on the other hand, change the size of a shape, but they preserve. ![]() Rigid transformationssuch as translations, rotations, and reflectionspreserve the lengths of segments, the measures of angles, and the areas of shapes. But points, lines, and shapes can be rotates by any point (not just the origin)! When that happens, we need to use our protractor and/or knowledge of rotations to help us find the answer. We often use rigid transformations and dilations in geometric proofs because they preserve certain properties. The rotation rules above only apply to those being rotated about the origin (the point (0,0)) on the coordinate plane. If we compare our coordinate point for triangle ABC before and after the rotation we can see a pattern, check it out below: Transformations are commonly found in algebraic functions. A reflection is a transformation that acts like a mirror: It swaps all pairs of points that are on exactly opposite sides of the line of reflection. Transformations can be represented algebraically and graphically. Here are the rules for transformations of function that could be applied to the graphs of functions. To derive our rotation rules, we can take a look at our first example, when we rotated triangle ABC 90º counterclockwise about the origin. On a coordinate grid, we use the x-axis and y-axis to measure the movement. Rotation Rules: Where did these rules come from? If the line of reflection was something else (like x -4), you would. ![]() Yes, it’s memorizing but if you need more options check out numbers 1 and 2 above! To reflect Triangle ABC across the y-axis, we need to take the negative of the x-value but leave the y-value alone, like this: A (-2, 6) B (-5, 7) C (-4, 4) Please note that the process is a bit simpler than in the video because the line of reflection is the actual y-axis.
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