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Select all transformations that carry rectangle

ABCD onto itself.


A. Rotate by 90 degrees clockwise using center P.


B. Rotate by 180 degrees clockwise using center P.


C. Reflect across line m.


D. Reflect across diagonal AC

.

E. Translate by the directed line segment from A to B.

User Antekone
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2 Answers

5 votes

Final answer:

Rotations of 180 degrees and reflections across a line of symmetry or a diagonal can map a rectangle onto itself.

Step-by-step explanation:

The transformations that can carry a rectangle onto itself include certain rotations and reflections that maintain the figure's congruence and orientation within a plane. Specifically:

B. Rotate by 180 degrees clockwise using center P is a transformation that would carry rectangle ABCD onto itself because a 180-degree rotation will map all corners back onto their original locations.

C. Reflect across line m, assuming line m is an axis of symmetry for the rectangle (for example, a median through the center of the rectangle), this reflection would also map the rectangle onto itself.

D. Reflect across diagonal AC, if AC is a diagonal of the rectangle, then reflecting the rectangle across this diagonal will also map it onto itself, as diagonals of a rectangle are axes of symmetry.

Rotating by 90 degrees (option A) will not map the rectangle onto itself unless ABCD is a square, which is a specific type of rectangle.

Similarly, translating by the directed line segment from A to B (option E) will move the rectangle to a new position, rather than mapping it onto itself.

User Liton
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2 votes
B it rotates by 180 degrees clockwise using center P.
User Jacob Nordfalk
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