Rectangle $JKML$ is rotated clockwise around point $P$ so that it maps onto itself. What is the smallest positive angle of rotation that will accomplish this?

• A. $180°$
• B. $360°$
• C. $45°$
• D. $90°$

Answer: (D)

Verified step by step guidance

1. Understand that the problem asks for the smallest positive angle of rotation about point P that maps rectangle JKML onto itself, meaning the rectangle looks exactly the same after rotation.
2. Recall that a rectangle has rotational symmetry of order 2, meaning it maps onto itself after a rotation of 180° about its center. However, the problem may involve rotation about a different point P, so consider the properties of the rectangle and its symmetries.
3. Recognize that rectangles also have rotational symmetry of 180° about their center, but if the rotation is about a vertex or another point, smaller angles might be possible depending on the rectangle's orientation and the point chosen.
4. Since the rectangle is a quadrilateral with right angles and opposite sides equal, rotating it by 90° about its center will map it onto itself because the shape and side lengths remain consistent after such rotation.
5. Conclude that the smallest positive angle of rotation that maps the rectangle onto itself is 90°, as rotating by 90° or multiples thereof (90°, 180°, 270°, 360°) will align the rectangle with its original position.