Determine the shortest distance from a house situated at the origin to a road that is represented by the line 3y+x+18=0
The shortest distance from a point P(x0,y0) to a line L: Ax+By+C = 0 is the length of the perpendicular from P to L.
The distance is given by:
D=(Ax0+By0+C)/√(A²+B²)
Although D may be positive or negative, take the absolute value (i.e. positive value).
Applying the formula, we get, for origin(0,0),
D=(3(0)+(0)+18)/√(3²+1²)
=18/√10