1. The problem statement, all variables and given/known data Determine the Miller indices of the cubic crystal plane that intersects the position coordinates C (1, 1/4, 0), A (1, 1, 1/2), B (3/4, 1, 1/4), and all coordinate axes. 3. The attempt at a solution This is an example problem with solution from Foundations of Materials Science and Engineering by Smith and Hashemi, so I already have the solution and I know the way to solve it. My only problem is the "and all coordinate axes" part of the problem. The authors create a point D, which of course has the y-coordinate 1 and z-coordinate 0. However, I have no idea how to find the x-coordinate, which they just write is 1/2, without any explanation. I tried thinking about this in a trigonometric way, but I cannot see that I have enough to solve it trigonometrically either. If anyone can explain to me how they conjured up the x-coordinate I would be very grateful!