Question

a rectangle is shown below. line m intersects two vertices. line n bisects each side it passes through. point k is the center of the rectangle. which transformation(s) must map the rectangle exactly onto itself? choose all that apply. clockwise rotation about k by 90°. reflection across line n. counterclockwise rotation about k by 180°. reflection across line m. none of the above

Explanation:

Step1: Analyze reflection across line m

A reflection across line m (which passes through two vertices) will map the rectangle onto itself because line m is a line of symmetry for the rectangle.

Step2: Analyze reflection across line n

A reflection across line n (which bisects the sides) will map the rectangle onto itself since line n is also a line of symmetry for the rectangle.

Step3: Analyze 180 - degree rotation about K

A 180 - degree counter - clockwise rotation about the center point K of the rectangle will map the rectangle onto itself as the rectangle has rotational symmetry of order 2 about its center.

Step4: Analyze 90 - degree rotation about K

A 90 - degree clockwise or counter - clockwise rotation about K will not map the rectangle onto itself as rectangles do not have 90 - degree rotational symmetry (except for squares which are a special case of rectangles, but this is a general rectangle).

Answer:

Reflection across line m, Reflection across line n, Counterclockwise rotation about K by 180°