Question

transformations test (topic 4)
quadrilateral abcd is mapped to quadrilateral abcd. which of the following transformations would not result in the two quadrilaterals being congruent?
a. a translation along side $overline{ab}$ by a distance of twice $overline{ab}$
b. a rotation about point c by 90 degrees counterclockwise
c. a dilation from point a by a factor of one - half
d. a reflection across side $overline{bc}$

Explanation:

To determine which transformation does not result in congruent quadrilaterals, we analyze each option:

• Translation: A translation is a rigid transformation (preserves distance and angle), so the image is congruent to the original.
• Rotation: A rotation about a point is also a rigid transformation, preserving congruence.
• Dilation: A dilation with a scale factor of one - half changes the size of the figure (it scales the lengths by 1/2). Congruent figures must have the same size and shape, so a dilation (except with scale factor 1) does not produce a congruent figure.
• Reflection: A reflection across a line is a rigid transformation, so the image is congruent to the original.

So the transformation that does not result in congruent quadrilaterals is the dilation from point A by a factor of one - half.

Answer:

A dilation from point A by a factor of one - half (the option: "A dilation from point A by a factor of one - half")