I would be inclined to set it up in a coordinate system- set the origin, (0, 0) , at A. If we take C to be at (0, Y) and B at (X, 0), then the line has equation \(\displaystyle \frac{x}{X}+ \frac{y}{Y}= 1\). Since it passes through (1, 1) we have \(\displaystyle \frac{1}{X}+ \frac{1}{Y}= 1\). Since BC= 4, \(\displaystyle X^2+ Y^2= 16\). Solve those two equations for X and Y.
