Question

which sequence of transformations results in figures that are similar but not congruent?a reflection across the x - axis, translation 7 units to the leftb 90° clockwise rotation, translation 5 units to the leftc reflection across the x - axis, dilation with a factor of 4d translation 3 units down, reflection across the y - axis

Explanation:

Step1: Recall the properties of congruent and similar figures

Congruent figures have the same shape and size. Similar figures have the same shape but not necessarily the same size. Transformations that preserve size (reflections, translations, rotations) result in congruent figures. Transformations that change size (dilations) result in similar - but - not - congruent figures when the scale factor is not \(1\).

Step2: Analyze each option

• Option A: Reflection across the \(x -\)axis (a rigid transformation that preserves size) and translation \(7\) units to the left (a rigid transformation that preserves size). The combined transformation is a rigid transformation, so the figures are congruent.
• Option B: \(90^{\circ}\) clockwise rotation (a rigid transformation that preserves size) and translation \(5\) units to the left (a rigid transformation that preserves size). The combined transformation is a rigid transformation, so the figures are congruent.
• Option C: Reflection across the \(x -\)axis (a rigid transformation that preserves size) and dilation with a factor of \(4\) (a non - rigid transformation that changes size). Since the scale factor \(k = 4

eq1\), the figures are similar but not congruent.

• Option D: Translation \(3\) units down (a rigid transformation that preserves size) and reflection across the \(y -\)axis (a rigid transformation that preserves size). The combined transformation is a rigid transformation, so the figures are congruent.

Answer:

C. reflection across the x - axis, dilation with a factor of 4