; This input arrives at the shortest distance between a point and a line ; in 2 dimensions. The point is at (x0, y0) in cartesian coordinates. ; (x, y) are the points on the line. a*x+b*y+c=0 ; equation of the line y ; solve for y unfactor fraction ; equation of the line in slope-intercept form: distance=|a*(x-x0)+b*(y-y0)|/(a^2+b^2)^.5 eliminate y ; Combine the above two equations to eliminate x and y. simplify ; The beautiful answer is: