Question

quadrilateral abcd is mapped to quadrilateral abcd. which of the following transformations would not result in congruent?
a dilation from point a by a factor of one - half
a rotation about point c by 90° counterclockwise
a translation along side $overline{ab}$ by a distance of twice ab
a reflection across side $overline{bc}$

Explanation:

Step1: Recall transformation properties

Rigid - motions (rotations, translations, reflections) preserve congruence. Dilations change the size.

Step2: Analyze each option

Rotations, translations, and reflections are rigid - motions. A dilation by a factor other than 1 changes the size of the figure. A dilation from point A by a factor of one - half will make the new quadrilateral half the size of the original, so it will not be congruent. Rotation about point C by 90° counterclockwise, translation along side $\overline{AB}$ by a distance of twice $AB$, and reflection across side $\overline{BC}$ are all rigid - motions and will result in congruent figures.

Answer:

a dilation from point A by a factor of one - half