Explanation Let A ′ B ′ C ′ D ′ be the rotation of the rectangle ABCD at 180 ° about point P . Since the given degree 180 ° is positive, the rotation should be in counterclockwise direction. The vertex A ′ of the rotated rectangle is in the same position as vertex C of the original rectangle. The vertex B ′ of the rotated rectangle is in the same position as vertex D of the original rectangle. The vertex C ′ of the rotated rectangle is in the same position as vertex A of the original rectangle. The vertex D ′ of the rotated rectangle is in the same position as vertex B of the original rectangle. Therefore, A ′ B ′ C ′ D ′ forms the 180 ° rotation of the rectangle ABCD . The graph of the 180 ° rotation of the rectangle ABCD is shown below in Figure 1

A Survey of Mathematics with Applications plus MyLab Math Student Access Card -- Access Code Card Package (10th Edition)

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ISBN: 9780134115764

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 8, Problem 44RE

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The rectangle ABCD have 180° rotational symmetry about the point P or not.

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Chapter 8, Problem 43RE

Chapter 8, Problem 45RE

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Use the Euclidean algorithm to find two sets of integers (a, b, c) such that 55a65b+143c: Solution = 1. By the Euclidean algorithm, we have: 143 = 2.65 + 13 and 65 = 5.13, so 13 = 143 – 2.65. - Also, 55 = 4.13+3, 13 = 4.3 + 1 and 3 = 3.1, so 1 = 13 — 4.3 = 13 — 4(55 – 4.13) = 17.13 – 4.55. Combining these, we have: 1 = 17(143 – 2.65) - 4.55 = −4.55 - 34.65 + 17.143, so we can take a = − −4, b = −34, c = 17. By carrying out the division algorithm in other ways, we obtain different solutions, such as 19.55 23.65 +7.143, so a = = 9, b -23, c = 7. = = how ? come [Note that 13.55 + 11.65 - 10.143 0, so we can obtain new solutions by adding multiples of this equation, or similar equations.]

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The rectangle ABCD have 180 ° rotational symmetry about the point P or not.

Solution Summary: The author determines whether the rectangle ABCD has 180° rotational symmetry about the point P.

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The rectangle ABCD have 180° rotational symmetry about the point P or not.

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