Find the point on the line y = 3x + 2 that is closest to the origin.

Question

(x, y) =

Answer 1

distance to the origin squared:

d²=(x-0)²+(y-0)² = x²+(3x+2)²=x²+9x²+12x+4 = 10x²+12x+4

Take the derivative, set to zero and solve for x

2dd' = 20x+12

d' =(20x-12)/2d = 0

x = -6/10

y = 3(-6/10)+2 = 2/10

(x,y) = (-0.6, 0.2)