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![]() ![]() Now, we know that 90° clockwise rotation will make the coordinates (x, y) be (y, -x). Solution: As you can see, triangle ABC has coordinates of A(-4, 7), B(-6, 1), and C(-2, 1). Rotate the triangle ABC about the origin by 90° in the clockwise direction. ![]() We can show it graphically in the following graph.Įxample 4: The following figure shows a triangle on a coordinate grid. So, for the point K (-3, -4), a 180° rotation will result in K’ (3, 4). Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Solution: As we know, 180° clockwise and counterclockwise rotation for coordinates (x, y) results in the same, (-x, -y). Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Show the plotting of this point when it’s rotated about the origin at 180°. It will look like this:Įxample 3: In the following graph, a point K (-3, -4) has been plotted. So, for this figure, we will turn it 180° clockwise. Solution: We know that a clockwise rotation is towards the right. How To Discover Rotation Rules Using discovery in geometry leads to better understanding. 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. ![]() The images are represented in the following graph.Įxample 2: In the following image, turn the shape by 180° in the clockwise direction. We often use rigid transformations and dilations in geometric proofs because they preserve certain properties. Thus, for point B (4, 3), 180° clockwise rotation about the origin will give B’ (-4, -3). Similarly, for B (4, 3), 90° clockwise rotation about the origin will give B’ (3, -4).ī) For clockwise rotation about the origin by 180°, the coordinates (x, y) become (-x, -y). 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