Question

1. a figure on the coordinate plane is transformed to create a new figure. determine whether each transformation preserves or does not preserve congruence. select the correct answer in each row. a reflection across the y - axis a rotation of 180°, counterclockwise with the origin as the center of rotation a dilation by a scale factor of 0.5 with the origin as the center of dilation preserves congruence does not preserve congruence

Explanation:

• Reflection across the y - axis: A reflection is a rigid transformation. Rigid transformations (reflections, rotations, translations) preserve the shape and size of a figure, so they preserve congruence. So this transformation should be in the "Preserves Congruence" column.
• Rotation of \(180^{\circ}\) counterclockwise with the origin as the center: Rotation is also a rigid transformation. It does not change the shape or size of the figure, so it preserves congruence. So this transformation should be in the "Preserves Congruence" column.
• Dilation by a scale factor of 0.5 with the origin as the center of dilation: Dilation changes the size of the figure (it scales the figure). Since congruent figures must have the same size and shape, dilation does not preserve congruence. So this transformation should be in the "Does Not Preserve Congruence" column.

Answer:

• A reflection across the y - axis: Preserves Congruence
• A rotation of \(180^{\circ}\) counterclockwise with the origin as the center of rotation: Preserves Congruence
• A dilation by a scale factor of 0.5 with the origin as the center of dilation: Does Not Preserve Congruence