# Find the point on the line y = 5x + 3 that is closest to the origin.?

• let the point (m , n) on the line y = 5x + 3 is closest to origin (0,0)

substituting x = m and y = n in eqn of line

n = 5m + 3

so The point is (m . 5m + 3)

The distance, s between [ m , (5m + 3) ] and (0, 0) is

s = √[m^2 + (5m+3)^2 ]

= √(m^2 + 25m^2 + 30m + 9)

= √(26m^2 + 30m + 9)

differentiate and equate it to zero

(1/2)[ 52m + 30] / √(26m^2 + 30m + 9) = 0

=> 52m + 30 = 0

m = -30 / 52

= -15/26

n = 5m + 3

= -(75/26) + 3

= 3/26

The closest point to origin = (-15/26, 3/26)