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 length. the perimeter of ( \triangle abc ) is perimeter of ( \triangle xyz ). the perimeter of ( \triangle abc ) is. a possible set of values of ab, bc, and ac is
(type a whole number.)

Explanation:

Step1: Properties of Transformations

Reflections and rotations preserve length. So, the perimeter of \(\triangle ABC\) is equal to the perimeter of \(\triangle XYZ\).

Step2: Determine Perimeter of \(\triangle ABC\)

Since the perimeter of \(\triangle XYZ\) is \(26\), the perimeter of \(\triangle ABC\) is also \(26\).

Step3: Find a Set of Side - Lengths

We need three positive whole numbers \(AB\), \(BC\), and \(AC\) such that \(AB + BC+AC = 26\). For example, if \(AB = 8\), \(BC = 9\), and \(AC = 9\) (because \(8 + 9+9=26\)).

Answer:

Reflections and rotations preserve length. The perimeter of \(\triangle ABC\) is equal to the perimeter of \(\triangle XYZ\). The perimeter of \(\triangle ABC\) is \(26\). A possible set of values of \(AB\), \(BC\), and \(AC\) is \(8\), \(9\), \(9\) (answers may vary as long as their sum is \(26\)).