Question

which transformation maps the parallelogram onto itself?
a. a 180° rotation about the origin
b. a 90° rotation about the origin
c. a reflection over the y - axis
d. a reflection over the x - axis

Explanation:

Step1: Recall properties of parallelograms

A parallelogram has rotational symmetry of order 2. A \(180^{\circ}\) rotation about the center (in this case, the origin) maps a parallelogram onto itself.

Step2: Analyze other transformations

• A \(90^{\circ}\) rotation (\(B\)): A non - square/non - rhombus parallelogram (as in the general case shown) will not map onto itself with a \(90^{\circ}\) rotation.
• Reflection over \(y\) - axis (\(C\)): The shape of the parallelogram (non - symmetric about \(y\) - axis in the general position) will not map onto itself.
• Reflection over \(x\) - axis (\(D\)): The shape of the parallelogram (non - symmetric about \(x\) - axis in the general position) will not map onto itself.

Answer:

A. a \(180^{\circ}\) rotation about the origin