Question

rectangle klmn is rotated 90° clockwise about the origin to form rectangle qrst. which statement is true? the length of segment rs is less than the length of segment lm because rotations decrease length. the opposite sides of rectangle qrst are parallel because rotations always preserve parallel lines. the length of segment ts is greater than the length of segment nm because rotations increase length. the opposite sides of rectangle qrst are not parallel because rotations do not preserve parallel lines.

Explanation:

Step1: Recall Rotation Properties

Rotations are rigid transformations, meaning they preserve side lengths and parallelism of lines. So options claiming rotations change length (first, fourth) or don't preserve parallelism (fifth) are wrong.

Step2: Analyze Each Option

• First option: Rotations don't decrease length. Eliminate.
• Second option: Rotations preserve parallel lines, so opposite sides of QRST (a rotated rectangle) remain parallel. This is correct.
• Third option: Rotations don't increase length. Eliminate.
• Fourth option: Rotations preserve parallelism. Eliminate.

Answer:

The opposite sides of rectangle QRST are parallel because rotations always preserve parallel lines.