Derive Distance Formula

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

Thanks

 

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



the distance formula is

 

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

 

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 )

 

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

 

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;
}

 

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.

 

\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

 

Ok. Thanks.