Reflection question

Question

This is a practice question to a test I will be taking soon. My conjecture is that it's none of the choices given. I tried reflections about y=x, y-axis, x-axis and it doesn't work. Does anyone agree?

Answer 1

The correct answer on the test should be $A$.

However, you could make a convincing argument for case $B$, because theoretically, you can do this with two reflections. You first reflect $ABC$ about $y=x$, so it is in the same location as $A'B'C'$. Then you set up a reflection along an axis that goes through the middle of the triangle (a straight line from negative $y$ to positive $x$) to reflect the triangle exactly such that all the points match.

I don't expect that sort of argument to be required.

Answer 2

If you use during the transformation odd number of reflection than final triangle would have opposite orientation ie. ABC would go in anti-clockwise order. This rules out II and III.

That the answer is I is already given by Newb.