Question

the composition of transformations $r_{y = - 5}circ r_{(90^{circ},a)}$ maps $\triangle abc$ to $\triangle xyz$. if the perimeter of $\triangle xyz$ is 26, what is a possible set of values of $ab$, $bc$, and $ac$? explain. reflections and rotations preserve length. the perimeter of $\triangle abc$ is blank perimeter of $\triangle xyz$. the perimeter of $\triangle abc$ is blank. a possible set of values of $ab$, $bc$, and $ac$ is blank (type a whole number.)

Explanation:

Step1: Recall transformation property

Reflections and rotations are rigid - motions which preserve length. So, the perimeter of the pre - image is equal to the perimeter of the image.

Step2: Determine perimeter of △ABC

Since the perimeter of △XYZ is 26 and reflections and rotations preserve length, the perimeter of △ABC is also 26.

Step3: Find possible side - lengths

We need to find three whole numbers that add up to 26. One possible set is 8, 9, 9 since \(8 + 9+9=26\).

Answer:

The perimeter of △ABC is equal to the perimeter of △XYZ. The perimeter of △ABC is 26. A possible set of values of AB, BC, and AC is 8, 9, 9.