# 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.

a*x+b*y+c=0 ; equation of the line
y ; solve for y
unfactor fully 1 ; equation of the line in slope-intercept form:
distance=|a*(x-x0)+b*(y-y0)|/(a^2+b^2)^.5
eliminate y
simplify ; the beautiful answer is: