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

Solution:

The point on the line y = 5x + 2 that is closest to the origin will be on the line perpendicular to the origin.

y = 5x + 2 [Given]

Slope = m₁ = 5

When two lines are perpendicular to each other

m₁ - m₂ = - 1

m₂ = -1 / m1

m₂ = -1/5

y = -1/5 x

Substitute the value of y in the given equation

-1/5 x = 5x + 2

-1/5 x - 5x = 2

Taking LCM

(-1 - 25) / 5 x = 2

-26/5 x = 2

By cross multiplication

x = 2 × -5/26

x = -5/13

y = - 1/5 (-5/13)

= 1/13

Therefore, the point on the line closest to the origin is (-5/13, 1/13).

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

Summary:

The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).