Find the point on the line 5x+4y+1=0 which is closest to the point (-2,-1).

Answer 1

The perpendicular (shortest) distance from a point to a line is given by the formula

d= (Ax₀+By₀+C)/sqrt(A²+B²) where the line is Ax + By + C = 0 and the point is (x₀,y₀).

The derivation of this formula can easily be found on the Internet, but it is too long to reproduce here.