Question

1. a triangle has vertices with the coordinates (1, 1), (3, 7), and (9, 7). the triangle is translated down 3 units and then reflected over the x - axis.

part a
graph the results of the transformation.
part b
which statement about the image and preimage is true?
a the image is congruent to the preimage because they are both scalene triangles.
b the image is congruent to the preimage because the sides are the same length.
c the image is not congruent to the preimage because the orientation of the triangle has changed.
d the image is not congruent to the preimage because the side lengths differ in measure.

Explanation:

Step1: Understand transformation properties

Translation (moving down 3 units) and reflection (over the x - axis) are rigid transformations. Rigid transformations preserve side - lengths and angles.

Step2: Analyze each option

• Option A: The reason "because they are both scalene triangles" is incorrect. Congruence is determined by side - lengths and angles, not the type of triangle (scalene, isosceles, etc.).
• Option B: Since translation and reflection are rigid transformations, they preserve side - lengths. So, the image and pre - image have sides of the same length, and the triangles are congruent.
• Option C: Orientation change does not affect congruence. Rigid transformations can change orientation (like reflection) but still keep the figures congruent.
• Option D: Rigid transformations do not change side - lengths. So, the side - lengths of the image and pre - image are equal.

Answer:

B. The image is congruent to the preimage because the sides are the same length.