Find the point on the line y = 5x + 2 that is closest to the origin.

Linear equations and graphs
asked 2021-06-12

Find the point on the line \(y = 5x + 2\) that is closest to the origin.

Answers (1)

let the point be \((x,5x+2)\)
We have to minimize
\(d = x^2 + (5x+2)^2\)
\(d' = 2x+ 10(5x+2) = 0\)
\(52x = -20\)
\(x=-\frac{10}{26} =-\frac{5}{13}\)
\(y = \frac{1}{13}\)
\((-\frac{5}{13} , \frac{1}{13})\)
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