Question

a rectangle is shown below. line m intersects two vertices. line n bisects each side it passes through. point y is the center of the rectangle. which transformation(s) must map the rectangle exactly onto itself? choose all that apply. reflection across line n reflection across line m counterclockwise rotation about y by 180° clockwise rotation about y by 270° none of the above

Explanation:

Step1: Analyze Reflection across line n

Line n bisects each side it passes through and Y is the center. A rectangle has reflection symmetry over a line through the mid - points of opposite sides (line n here). So reflecting across line n will map the rectangle onto itself.

Step2: Analyze Reflection across line m

Line m intersects two vertices. A rectangle does not have reflection symmetry across a diagonal (line m is a diagonal here), so reflection across line m will not map the rectangle onto itself.

Step3: Analyze 180° rotation about Y

A rectangle has rotational symmetry of order 2 about its center (Y). Rotating 180° about Y will map each vertex to the opposite vertex, so the rectangle maps onto itself.

Step4: Analyze 270° clockwise rotation about Y

A rectangle rotated 270° clockwise about its center will not map onto itself (it has rotational symmetry for 180° and 360° in terms of mapping exactly, 90° and 270° rotations do not preserve the rectangle's orientation in a way that it maps onto itself).

Answer:

Reflection across line n, Counterclockwise rotation about Y by 180°