# Derive Distance Formula

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

1. ### 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

2. ### MathLover1

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

the distance formula is

MathLover1, Jul 29, 2021
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3. ### nycmathguy

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Very cool. There's another formula involving the variable z. Look for a separate thread.

nycmathguy, Jul 29, 2021
4. ### 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

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Very cool. Do you know LaTex? If you do, can you teach me the basics?

nycmathguy, Jul 30, 2021
6. ### 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

#include <iostream>

int main() {
std::cout << "Hello World!";
return 0;
}

MathLover1, Jul 30, 2021
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7. ### 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
8. ### 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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