Question

1. a transformation is applied to a figure to create a new figure. which transformation does not preserve congruence? a reflection across the x-axis a translation 7 units down a dilation by a scale factor of 5 a rotation of 90° clockwise

Explanation:

Step1: Recall congruence-preserving transformations

Reflections, translations, and rotations are rigid transformations. Rigid transformations preserve the shape and size of a figure, so they preserve congruence.

Step2: Analyze dilation

Dilation is a non - rigid transformation. A dilation by a scale factor of 5 will change the size of the figure (it will stretch or shrink the figure). Since congruent figures must have the same size and shape, a dilation does not preserve congruence.

Step3: Evaluate each option

• Option A: Reflection across the x - axis is a rigid transformation, so it preserves congruence.
• Option B: Translation 7 units down is a rigid transformation, so it preserves congruence.
• Option C: Dilation by a scale factor of 5 is a non - rigid transformation, so it does not preserve congruence.
• Option D: Rotation of \(90^{\circ}\) clockwise is a rigid transformation, so it preserves congruence.

Answer:

C. A dilation by a scale factor of 5