Question

1. a triangle with vertices (1,1), (3,1), (2,4) is translated using the rule (x - 2, y + 2). what are the new coordinates of the triangle?
2. which transformation always produces a congruent figure?

a) reflection
b) rotation
c) translation
d) all of the above

Explanation:

Step1: Apply rule to first vertex

For vertex (1,1), using the rule (x - 2,y + 2), we have x=1,y = 1. New x is 1-2=-1, new y is 1 + 2=3. So new vertex is (-1,3).

Step2: Apply rule to second vertex

For vertex (3,1), with x = 3,y = 1. New x is 3-2=1, new y is 1+2=3. So new vertex is (1,3).

Step3: Apply rule to third vertex

For vertex (2,4), when x = 2,y = 4. New x is 2-2=0, new y is 4+2=6. So new vertex is (0,6).

Step1: Recall congruent - transformation properties

Reflections, rotations, and translations are rigid - motions. Rigid motions preserve side - lengths and angle - measures. So, they produce congruent figures.

Answer:

A. (-1,3), (1,3), (0,6)