Find the point on the line y = 5x + 3 that is closest to the origin.?
What is the point on the line defined by the equation y = 5x + 3 that is closest to the origin (0, 0)?
2 Answers
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)
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