Vector calculus: Given n points (x1,y1),(xn,yn) on plane, apply calculus tools to...

resilient_hawk

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Hi, I would need help with this question. I do not even know where or what should I start with. Here's the question and I would greatly appreciate your help.

Part 1:Given n points (x1,y1),,(xn,yn) on the plane, apply calculus tools to find equations on the point (x,y) that minimizes the sum of distances from (x,y) to the given points. You should formulate your answer in terms of vectors
r1,r2,,rn,
where ri is the unit vector that points from (x,y) to (xi,yi) for all i=1,2,,n.

Part 2:

Screenshot (118).jpg
 
The geometric median is the point that minimizes the sum of distances to a finite set of points. As far as I know, there is no closed form formula for the geometric median. However, the problem of finding the point that minimizes the sum of squared distances to a finite set of points does have a closed form formula that can be derived with calculus. Any chance the there's a typo in the question?
 
The geometric median is the point that minimizes the sum of distances to a finite set of points. As far as I know, there is no closed form formula for the geometric median. However, the problem of finding the point that minimizes the sum of squared distances to a finite set of points does have a closed form formula that can be derived with calculus. Any chance the there's a typo in the question?

This is an excellent point. The OP may want to read about the geometric median, for example here.

But I notice that the problem doesn't actually say to solve for (x,y); it just says to "apply calculus tools to find equations" that describe the point.

Resilient_hawk, can you tell us what tools you have learned, and show us how you tried to use them?

Also, the image says, "Explain how your answer for n=3 and n=4 is consistent with what you learned from the lecture." We can't help with that until you tell us what you learned from the lecture -- and that would probably help us see what you are expected to do, as well. This is part of what it means to tell us the whole problem, and to show your work, in order to get help. (See our Read Before Posting announcement.)
 
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