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Homework Help: Minimize distance between three points.

  1. Apr 14, 2013 #1
    Find the value of m such that the sum of the squares of the vertical distances from each of the points (1,1) , (2,2) , and (3,2) to the line y=mx is minimized. Hint: Find the sum as a function of m (no x in the expression) and then minimize it.

    Distance equation. d=[itex]\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}[/itex]

    So, our professor made it easier on use and since we have single variable calculus the distance to be found is vertical to the line y=mx. Therefore, the x values will cancel out and we will only be interested in the y values. With this knowledge I set out and tried to set up an equation for the distance formula for each of the values given; but, x values were given in the equation I used for the distance values when I subbed the y value for mx. I'm not sure how to juggle these three equations. How would you proceed with solving this equation. Thank you.
  2. jcsd
  3. Apr 15, 2013 #2


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    2017 Award

    Staff: Mentor

    Can you show what you did?

    Add them. The sum of the squared distances should be minimized.
  4. Apr 15, 2013 #3
    How would you express the vertical distance between a given point [tex](x_{1},y_{i})[/tex] and a point on the line y=mx. (hint, what is the vertical distance between the y values ?).
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