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 2 units up followed by a translation of 2 units to the left a reflection across the y-axis followed by a rotation about the origin of 10 a rotation about the origin of 50° followed by a dilation with a scale factor of 8 a dilation with a scale factor of 0.6 followed by a translation of 2 units up

Explanation:

1. Recall the definitions: Congruent figures have the same shape and size; similar figures have the same shape but not necessarily the same size. Transformations that preserve size (translation, reflection, rotation) produce congruent figures. Dilation changes the size (scale factor ≠ 1) and produces similar (not congruent, if scale factor ≠ 1) figures.
2. Analyze each option:

• First option: Two translations. Translations preserve size, so the figure is congruent. Eliminate.
• Second option: Reflection and rotation. Both preserve size, so the figure is congruent. Eliminate (note: "rotation about the origin of 10" likely a typo, but reflection + rotation are rigid motions).
• Third option: Rotation (rigid, preserves size) followed by dilation (scale factor 8 ≠ 1, changes size). So the result is similar (same shape) but not congruent (different size). Include.
• Fourth option: Dilation (scale factor 0.6 ≠ 1, changes size) followed by translation (rigid). Dilation makes it similar (not congruent), translation doesn't affect similarity/congruence. Include.

Answer:

• a rotation about the origin of \( 50^\circ \) followed by a dilation with a scale factor of 8
• a dilation with a scale factor of 0.6 followed by a translation of 2 units up