Question

a translation 3 units down, reflection across the y - axis b reflection across the x - axis, translation 7 units to the left c reflection across the x - axis, dilation with a factor of \\( \frac { 1 } { 2 } \\). d \\( 90 ^ { \circ } \\) clockwise rotation, translation 5 units to the left which sequence of transformations results in figures that are similar but not congruent?

Explanation:

Step1: Recall the properties of transformations

Congruent figures have the same shape and size. Similar figures have the same shape but not necessarily the same size.

• Translation: It is a rigid transformation (size and shape remain the same).
• Reflection: It is a rigid transformation (size and shape remain the same).
• Rotation: It is a rigid transformation (size and shape remain the same).
• Dilation: Changes the size of a figure (if the scale factor \(k

eq1\)). If two figures are related by a dilation (with \(k
eq 1\)) and other rigid transformations (reflection, translation, rotation), they are similar but not congruent.

Step2: Analyze each option

• Option A: Translation and reflection are rigid transformations. Figures related by translation and reflection are congruent.
• Option B: Reflection and translation are rigid transformations. Figures related by reflection and translation are congruent.
• Option C: Reflection (rigid transformation) and dilation (non - rigid transformation with scale factor \(k = \frac{1}{2}\)). Since there is a dilation with \(k=\frac{1}{2}

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

• Option D: Rotation (rigid transformation) and translation (rigid transformation). Figures related by rotation and translation are congruent.

Answer:

C. reflection across the x - axis, dilation with a factor of \(\frac{1}{2}\)