Question

which sequence of transformations would result in a figure that is similar, but not congruent, to the original figure? select all that apply. a translation 5 units down followed by a reflection across the y - axis a reflection across the y - axis followed by a dilation with a scale factor of 5. a rotation about the origin of 270° followed by a translation up 2 units. a dilation with a scale factor of 0.75 followed by a translation 3 units down.

Explanation:

Step1: Recall transformation properties

Translation, reflection and rotation are rigid - motions. They preserve congruence. Dilation changes the size.

Step2: Analyze each option

• Option 1: Translation 5 units down and reflection across the y - axis are rigid - motions. The figure will be congruent.
• Option 2: Reflection across the y - axis (rigid - motion) followed by dilation with a scale factor of 5 (non - rigid, changes size). The figure will be similar but not congruent.
• Option 3: Rotation about the origin of 270° and translation up 2 units are rigid - motions. The figure will be congruent.
• Option 4: Dilation with a scale factor of 0.75 (non - rigid, changes size) followed by translation 3 units down (rigid - motion). The figure will be similar but not congruent.

Answer:

B. a reflection across the y - axis followed by a dilation with a scale factor of 5; D. a dilation with a scale factor of 0.75 followed by a translation 3 units down