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 can also be used to map Figure 2 onto itself?
A. A reflection over a line through the center of the figure that is parallel to one of the sides of the figure.
B. A rotation of 90° clockwise about the center of the figure.
C. A reflection over one of the diagonals of the figure.
D. A rotation of 180° about the center of the figure.

We want to see which transformation maps a rhombus into itself and a rectangle into itself.

The correct option D, a rotation of 180° about the center of the figure.

So we have two figures that are parallelograms, but neither are a square. This means that rotations of 90° will not map the figures into the same figures, as for example, for the rectangle, a rotation of 90° changes the length into the width.

But if we apply another rotation of 90°, we have that change again, this means that after two rotations of 90° (or a single rotation of 180°) we map the length into the length and the width into the width (same thing for the rhombus).

Then the transformation that maps the figures into the same figure is a rotation of 180° about the center of the figure, thus the correct option is D.

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Option (D)

Step-by-step explanation:

Figure (1) is a rhombus and figure (2) is a rectangle.

Figure (1) will overlap onto itself by the rotation of 180° about the center.

Figure (2) will overlap onto itself by 2 possible ways.

1). Reflection across a line passing through the center of the figure and parallel to one of the sides.

2). Rotation of the figure by 180° about the center.

Therefore, common transformation of both the figures will be,

A rotation of 180° about the center.

Option (D) will be the answer.

r and t.

both are 64 degrees.