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

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Dr. Juanita Wolff

Feb 20, 2025

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 linen = 5m + 3so The point is (m . 5m + 3)The distance, s between [ m , (5m + 3) ] and (0, 0) iss = √[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 = 0m = -30 / 52= -15/26n = 5m + 3 = -(75/26) + 3= 3/26The closest point to origin = (-15/26, 3/26)... Show More
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