Derive Distance Formula

Discussion in 'Algebra' started by nycmathguy, Jul 29, 2021.

  1. nycmathguy

    nycmathguy

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    Derive the distance formula for points on the xy-plane. Show steps along the way.

    Thanks
     
    nycmathguy, Jul 29, 2021
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  2. nycmathguy

    MathLover1

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    Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry.


    [​IMG]
    the distance formula is


    [​IMG]
     
    MathLover1, Jul 29, 2021
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  3. nycmathguy

    nycmathguy

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    Very cool. There's another formula involving the variable z. Look for a separate thread.
     
    nycmathguy, Jul 29, 2021
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  4. nycmathguy

    MathLover1

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    almost same, just add z[1] and z[2]

    the distance between points (x1, y1, z1) and (x2, y2, z2) is given by:

    d=sqrt((x[2]-x[1])^2+(y[2]-y[1])^2+(z[2]-z[1])^2 )
     
    MathLover1, Jul 29, 2021
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  5. nycmathguy

    nycmathguy

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    Very cool. Do you know LaTex? If you do, can you teach me the basics?
     
    nycmathguy, Jul 30, 2021
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  6. nycmathguy

    MathLover1

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    No, I don’t know LaTeX. But I know it is a software system for document preparation.
    LaTeX is not a word processor! Instead, LaTeX encourages authors not to worry too much about the appearance of their documents but to concentrate on getting the right content.

    So, in LaTeX you would input this document as:

    \documentclass{article}
    \title{Cartesian closed categories and the price of eggs}
    \author{Jane Doe}
    \date{September 1994}
    \begin{document}
    \maketitle
    Hello world!
    \end{document}

    I know C++, and here is C++ "Hello World!" Program

    // Your First C++ Program

    #include <iostream>

    int main() {
    std::cout << "Hello World!";
    return 0;
    }
     
    MathLover1, Jul 30, 2021
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  7. nycmathguy

    nycmathguy

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    I know that LaTex is used to form math symbols.
    I don't mind using x^2 to represent the squaring of x, for example, but it is so much better when LaTex or MathMagic Lite is used.
     
    nycmathguy, Jul 30, 2021
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  8. nycmathguy

    MathLover1

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    \alpha
    \pm
    https://www.math.uci.edu/~xiangwen/pdf/LaTeX-Math-Symbols.pdf

    ...
    This formula $f(x) = x^2$ is an example.
    ...
    sample code for siple equation:

    \documentclass{article}

    \usepackage{amsmath}

    \begin{document}

    \begin{equation*}
    1 + 2 = 3
    \end{equation*}

    \begin{equation*}
    1 = 3 - 2
    \end{equation*}

    \begin{align*}
    1 + 2 &= 3\\
    1 &= 3 - 2
    \end{align*}

    \end{document}

    Output Equation:
    1+2=3
    1=3–2
     
    MathLover1, Jul 30, 2021
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  9. nycmathguy

    nycmathguy

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    Ok. Thanks.
     
    nycmathguy, Jul 30, 2021
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