Calculus Problem

Question

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

Answer 1

The closest point shall be on the normal (perpendicular) to the line.

y = 2x - 4. slope of line is 2

]-1/2 is slope of normal

(y + 5) = -(x + 5) / 2

y + 5 = -x/2 + 2.5

y = -x/2 - 2.5, equation of normal

Now determine point of intersection of given line and normal. That is the closest point.