# Reflection problem

I see one of the problems of my transformational geometry text book in the topic of reflection, i.e.:

there are two parallell lines g and h and two different points A and B. Both points are inside the area bounded by the lines. Draw the shortest route from A to g then to h then to B!

I assume, of course, we have to apply reflection, i.e. reflect A on g resulting A' and reflect B on h resulting B' then connect A' to B' implying there are two points C and D from the intersection of A'B' and g and A'B' and h respectively. So the shortest route is ACDB.

My question is that is my work correct? if yes, can anybody help with the reason? and if it is incorrect, please show the true work.

And $\overline {A'B'} = \overline {AC} + \overline {CD} + \overline {DB}$