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------------------------------------------------ Rotate the pentagon 180° clockwise about point Q.

A. The pentagon will be unchanged.
B. The pentagon will be inverted.
C. The pentagon will be shifted to the left.
D. The pentagon will be shifted to the right.

Rotating a pentagon 180° clockwise about a point will invert the pentagon. This is because a 180° rotation is equivalent to flipping the figure over its central point creating a mirror image. So the correct option is B.

Explanation:

This question pertains to the topic of geometry, specifically rotations. When a pentagon is rotated 180° clockwise about a point, this rotation is essentially an half-circle rotation around the given point. Consequently, this movement is the same as flipping the figure over, or creating a mirror image of it, but along its central point instead of a line of symmetry. Therefore the correct answer is: (b) The pentagon will be inverted.

Let's understand this with an example. If Point Q is the center of the pentagon, imagine a line drawn from any corner of the pentagon to point Q. Now imagine rotating the line 180°; the pentagon will appear flipped or upside down compared to the original orientation because its position relative to point Q has been inverted. Rotation, essentially, changes the position of the shape, not its shape or size.

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