Question

find all transformations that can be used to map the figure onto itself. select all that apply.
reflection over a horizontal line through the center
a rotation of 180°
a rotation of 90°
a rotation of 270°
reflection over a vertical line through the center

Explanation:

Step1: Analyze reflection

• A reflection over a horizontal line through the center: The figure is not symmetric about a horizontal line through the center.
• A reflection over a vertical line through the center: The figure is not symmetric about a vertical line through the center.

Step2: Analyze rotation

• A rotation of \(90^{\circ}\): The figure does not map onto itself after a \(90^{\circ}\) rotation.
• A rotation of \(270^{\circ}\): The figure does not map onto itself after a \(270^{\circ}\) rotation.
• A rotation of \(180^{\circ}\): For any quadrilateral (assuming it is a general quadrilateral - since no specific type like parallelogram etc. is indicated, but rotation by \(180^{\circ}\) about the center of the figure (mid - point of the line segment joining the mid - points of the diagonals) will map the figure onto itself.

Answer:

a rotation of \(180^{\circ}\)