Hi

Yes you are supposed to find a new point that would create the shortest sum of the distances AC+BC, C being on X-axis

The solution is given in the sketch below

A' being the symmetric point of A with respect to X-axis

A'C=AC

AC+BC=A'C+BC

This latter distance is shortest when A',B and C are aligned

This problem is also known as "the problem of the river" : suppose that you are in A and you want to go to B after getting some water at the river (X-axis), where do you have to get the water in order to minimize the global distance ?