Find the point on the line 6 x + 3 y + 2 = 0 which is closest to the point ( − 3 , 5 )

Answer 1

The shortest distance is measured along the perpendicular

y = -2x + 2/3

y_perp = x/2 + b

5 = -3/2 + b

13/2 = b

y_perp = x/2 + 13/2

The solution to y and y_perp is the point required.