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

Solution:

The point on the line y = 5x + 3 that is closest to the origin will be on the line perpendicular to the origin.

y = 5x + 3 [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 + 3

- 1/5 x - 5x = 3

Taking LCM

(-1 - 25)/5 x = 3

-24/5 x = 3

By cross multiplication

x = 3 × -5/25

x = -15/25

y = - 1/5 (-15/25) = 3/25

Therefore, the point on the line closest to the origin is (-15/25, 3/25).

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

Summary:

The point on the line y = 5x + 3 that is closest to the origin is (-15/25, 3/25).