Question

If a transformation maps two parallel lines to two image lines that are also parallel, we say that parallelism is invariant under the transformation. Is parallelism invariant under a reflection?

Short answer

Yes, parallelism is invariant under reflection.

Step-by-step solution

Step 1. Given Information.

The given statement is that if a transformation maps two parallel lines to two image lines that are also parallel.

Step 2. Explanation.

Yes, parallelism is invariant under reflection because distance is preserved under reflection and inclination of two lines with respect to each other is also preserved under reflection.

Step 3. Conclusion.

So, yes, parallelism is invariant under reflection.