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 origin.

Answer 1

B.

The first rectangle has side lengths 3 (from x=1 to x=4) and 4 (from y=-1 to y=3). Rotating a point (x,y) by 180° about the origin gives (-x,-y). Applying this to the first rectangle's vertices:
(1,-1)→(-1,1), (1,3)→(-1,-3), (4,3)→(-4,-3), (4,-1)→(-4,1),
which are exactly the vertices of the second rectangle. Thus they are congruent by a 180° rotation.