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How do you prove the Center Of Symmetry? - Answers

To prove the center of symmetry for a geometric figure, you must show that for every point in the figure, there exists a corresponding point that is equidistant from the center but in the opposite direction. Mathematically, if a point ( P(x, y) ) is in the figure, then the point ( P'(-x, -y) ) should also be in the figure for it to have a center of symmetry at the origin. If this condition holds true for all points in the figure, then it confirms that the figure has a center of symmetry. Alternatively, you can verify that the figure remains unchanged under a 180-degree rotation about the center.



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How do you prove the Center Of Symmetry? - Answers

https://math.answers.com/math-and-arithmetic/How_do_you_prove_the_Center_Of_Symmetry

To prove the center of symmetry for a geometric figure, you must show that for every point in the figure, there exists a corresponding point that is equidistant from the center but in the opposite direction. Mathematically, if a point ( P(x, y) ) is in the figure, then the point ( P'(-x, -y) ) should also be in the figure for it to have a center of symmetry at the origin. If this condition holds true for all points in the figure, then it confirms that the figure has a center of symmetry. Alternatively, you can verify that the figure remains unchanged under a 180-degree rotation about the center.



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https://math.answers.com/math-and-arithmetic/How_do_you_prove_the_Center_Of_Symmetry

How do you prove the Center Of Symmetry? - Answers

To prove the center of symmetry for a geometric figure, you must show that for every point in the figure, there exists a corresponding point that is equidistant from the center but in the opposite direction. Mathematically, if a point ( P(x, y) ) is in the figure, then the point ( P'(-x, -y) ) should also be in the figure for it to have a center of symmetry at the origin. If this condition holds true for all points in the figure, then it confirms that the figure has a center of symmetry. Alternatively, you can verify that the figure remains unchanged under a 180-degree rotation about the center.

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      To prove the center of symmetry for a geometric figure, you must show that for every point in the figure, there exists a corresponding point that is equidistant from the center but in the opposite direction. Mathematically, if a point ( P(x, y) ) is in the figure, then the point ( P'(-x, -y) ) should also be in the figure for it to have a center of symmetry at the origin. If this condition holds true for all points in the figure, then it confirms that the figure has a center of symmetry. Alternatively, you can verify that the figure remains unchanged under a 180-degree rotation about the center.

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