If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?

Taking that line XY is a line inside triangle ABC where Y lies on line BC and X lies on line AC.

As triangle ABC and XYZ are supposedly similar which should have been given in question to solve it.

The ratio of sides of similar triangles should be equal

So AC/XC=BC/YC

now BC=BY+YC BC=4+7=11

So

AC/10=11/7 or 7/11=10/AC

the above ratio would be required for calculation of AC