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Math Help - Finding the distance between two points

  1. #1
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    Finding the distance between two points

    Let Q = (0,5) and R = (10,6) be given points in the plane. We want to find the point P = (x,0) on the x axis such that the sum of distances PQ+PR is as small as possible.
    To solve this problem, we need to minimize the following function of x: f(x) = ?
    over the closed interval [A,B] where A = ? and B = ?
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  2. #2
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    Quote Originally Posted by derekjonathon View Post
    Let Q = (0,5) and R = (10,6) be given points in the plane. We want to find the point P = (x,0) on the x axis such that the sum of distances PQ+PR is as small as possible.
    To solve this problem, we need to minimize the following function of x: f(x) = ?
    over the closed interval [A,B] where A = ? and B = ?
    PQ = d_1

    d_1 = \sqrt{(x-0)^2 + (0-5)^2}


    PR = d_2

    d_2 = \sqrt{(x-10)^2 + (0-6)^2}

    d_1 + d_2 = S

    find \frac{dS}{dx} and minimize
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  3. #3
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    Still not getting it...

    Thank you for your help, I really appreciate it...

    But I am still not getting what the technique is here to answer the question.

    I understand finding distance (d1) and distance (d2)

    but the derivative part has me thrown off. Also, I don't get what function is supposed to be minimized...

    How do I go step by step through this?
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  4. #4
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    Quote Originally Posted by derekjonathon View Post
    Thank you for your help, I really appreciate it...

    But I am still not getting what the technique is here to answer the question.

    I understand finding distance (d1) and distance (d2)

    but the derivative part has me thrown off. Also, I don't get what function is supposed to be minimized...

    How do I go step by step through this?
    minimize the function S = \sqrt{x^2+25} + \sqrt{x^2-20x+136}

    start by finding \frac{dS}{dx}, set the result equal to 0, and solve for the value of x that minimizes S.
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