Question

figure 1 is a rhombus and figure 2 is a rectangle. neither figure is a square. which transformation can be used to map figure 1 onto itself and to map figure 2 onto itself? a. a rotation of 180° about the center of the figure b. a rotation of 90° clockwise about the center of the figure c. a reflection over a line through the center of the figure that is parallel to one of the sides of the figure d. a reflection over one of the diagonals of the figure

Explanation:

• For a rhombus: A rotation of \(180^{\circ}\) about its center maps it onto itself. The opposite sides and angles are congruent, and this rotation swaps the positions of the vertices in a way that the shape remains unchanged.
• For a rectangle: A rotation of \(180^{\circ}\) about its center also maps it onto itself. The opposite sides are equal and parallel, and this rotation preserves the shape's structure.
• Option B: A \(90^{\circ}\) clockwise rotation about the center will not map a non - square rhombus (since the angles are not \(90^{\circ}\)) or a non - square rectangle (as the adjacent sides are not equal) onto themselves.
• Option C: A reflection over a line through the center parallel to a side will not map a rhombus (which has symmetry about its diagonals, not about lines parallel to sides in the non - square case) onto itself.
• Option D: A reflection over a diagonal will not map a rectangle (a rectangle's diagonals are equal but a reflection over a diagonal will change the orientation of the sides in a non - square rectangle) onto itself.

Answer:

A. a rotation of \(180^{\circ}\) about the center of the figure