What is the distance from the origin to the point on the line $y = - 2 x + 5$ $y=-2x+5$ that is closest to the origin?

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What is the distance from the origin to the point on the line $y = - 2 x + 5$ $y=-2x+5$ that is closest to the origin?

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Answer 1 · 2018-04-25T16:47:08

$\sqrt{5}$ $sqrt{5}$

Explanation:

Our line is

$y = - 2 x + 5$ $y = -2x + 5$

We get the perpendiculars by swapping coefficients on $x$ $x$ and $y$ $y$ , negating one of them. We're interested in the perpendicular through the origin, which has no constant.

$2 y = x$ $2y = x$

These meet when $y = - 2 (2 y) + 5 = - 4 y + 5$ $y = -2(2y) + 5 = -4y + 5$ or $5 y = 5$ $5y =5$ or $y = 1$ $y=1$ so $x = 2$ $x=2$ . $(2.1)$ $(2.1)$ is the closest point, $\sqrt{2^{2} + 1} = \sqrt{5}$ $sqrt{2^2+1}=sqrt{5}$ from the origin.

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What is the distance from the origin to the point on the line $y = - 2 x + 5$ $y=-2x+5$ that is closest to the origin?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

What is the distance from the origin to the point on the line y=−2x+5y=-2x+5 that is closest to the origin?

1 Answer

Explanation:

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Impact of this question

What is the distance from the origin to the point on the line $y = - 2 x + 5$ $y=-2x+5$ that is closest to the origin?