Question

adelyn wants to make a copy of her trapezoid by using a two - step sequence of transformations. which sequence of transformations would produce a figure congruent to adelyns trapezoid?
option 1: a dilation of scale factor 4 centered at the origin followed by a reflection about the x - axis
option 2: a translation 10 units to the right followed by a dilation of scale factor 3 centered at the origin
option 3: a translation 10 units to the right followed by a rotation 180° counterclockwise about the origin
option 4: a dilation of scale factor 4 centered at the origin followed by a translation 1 unit up

Explanation:

Step1: Recall congruent transformation rules

Congruent figures have the same shape and size. Transformations that preserve size and shape are translations, rotations, reflections (rigid transformations). Dilations change size (scale factor ≠ 1), so sequences with dilation (scale factor ≠ 1) won't produce congruent figures.

Step2: Analyze each option

• Option 1: Dilation (scale 4) changes size → Not congruent.
• Option 2: Dilation (scale 3) changes size → Not congruent.
• Option 3: Translation (rigid) and rotation (rigid) → Both preserve size/shape. So this sequence produces congruent figure.
• Option 4: Dilation (scale 4) changes size → Not congruent.

Answer:

a translation 10 units to the right followed by a rotation \( 180^\circ \) counterclockwise about the origin