(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What point on the line y=3x-1 is closest to the origin? What is the distance to the origin from this point?

2. Relevant equations

3. The attempt at a solution

OK, I thought I knew how to do this but I don't think my answer seems right.

I find the normal vector to this line to be n=[3, -1]. I find an arbitrary point on the line by imputing x=1 into the equation and getting y=2 (so the point on the line is (1,2)). Then I subtract the vector of the origin (0,0) from that to get a random vector from the origin to a random point on the line. This vector is w=[1,2].

So to get the point on the line I do the projection of w onto n. My answer is [(3/11),(-1/11)]. This is the shortest vector from the origin to the line.. right? Can someone just double check this for me?

So then to get the point on the line.. I thought I should plug (3/11) into the original equation and get an answer for y but I get y=-2/11. Does this seem right?

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# Homework Help: What point on the line y=3x-1 is closest to the origin? What is the distance?

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