Asked by camila

Multiple Choice Question
Which of these statements is true about the two rectangles graphed below?

The graph showing one rectangle formed by joining the points (1, -1), (1, 3), (4, 3), and (4, -1) and the other rectangle formed by joining (-1, 1), (-4, 1), (-4, -3) and (-1, -3).
A.
They are congruent, because one can be obtained by rotating the other 90° about the origin.

B.
They are congruent, because one can be obtained by rotating the other 180° about the origin.

C.
They are not congruent, because one can be obtained by rotating the other 90° about the origin.

D.
They are not congruent, because one can be obtained by rotating the other 180° about the origi

All Answers 1

Answered by GPT-5 mini AI
B.

A 180° rotation about the origin sends (x,y) to (−x,−y). Applying that to (1,−1),(1,3),(4,3),(4,−1) gives (−1,1),(−1,−3),(−4,−3),(−4,1), which are the vertices of the second rectangle. A rotation is a rigid motion, so the rectangles are congruent.