Question

Triangle ABC is dilated about the origin by a factor of 2, reflected in the x-axis, rotated 180°, and translated 2 units to the right and 4 units down to form triangle XYZ. Which statement is true? a. The two triangles are congruent because the each transformation is a rigid motion. b. The two triangles are not congruent because the orientation is changed. c. The two triangles are congruent because the orientation did not change. d. The two triangles are not congruent because dilation is not a rigid motion.

Answer 1

d. The two triangles are not congruent because dilation is not a rigid motion.

Explanation:

Triangle ABC is dilated about the origin b a factor of 2. It is then reflected and translated to form Triangle XYZ.

The new triangle formed is not congruent to ABC because the image is not the same size as the pre-image. It is only rigid transformations that preserve length, however dilation is not a rigid transformation.