The regular octagon does not have point symmetry, and the statement "The regular octagon will map point C onto point E when rotated about point P 180°" is true. (option d)
Point symmetry, also known as reflectional symmetry, is a property where a figure can be divided into two equal halves by a single line, such that each half mirrors the other. The first statement, "A is the point of symmetry," is inaccurate. A regular octagon does not have a single point of symmetry that divides it into identical halves.
The second statement, "The regular octagon does not have point symmetry," is correct. Due to its even number of sides and angles, a regular octagon cannot possess point symmetry.
The third statement involves rotational symmetry. Rotational symmetry occurs when a figure can be rotated by a certain angle and still appear unchanged. The statement "The regular octagon will map point A onto point E when rotated about point P 180°" is incorrect. A 180° rotation about point P would not map point A onto point E; instead, it would map point A onto itself.
The final statement, "The regular octagon will map point C onto point E when rotated about point P 180°," is accurate. A 180° rotation about point P in a regular octagon would indeed map point C onto point E, as these points are symmetrically positioned with respect to the rotation center.
Hence the correct option is (d).
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