# 2D Coordinate Geometry - Problem Solving

###### This wiki is incomplete.

This page shows several examples for solving 2D coordinate geometry problems.

## Examples

The most used formula about this is the distance formula. If you want to find the distance between $(x_1,y_1)$ and $(x_2,y_2)$, you may use the distance formula

$\text{distance}=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt{(\triangle x)^2+(\triangle y)^2}.$

The midpoint formula might come in handy, too. The midpoint of $(x_1,y_1)$ and $(x_2,y_2)$ is

$\left(\frac{x_1+x_2}2,\frac{y_1+y_2}2\right).$

## Equation of Lines

The equation of lines is in the form of $y=mx+n$ (where $m$ is the slope and $n$ is the y-intercept), or $ax+by=c$.

What is the equation of the line passing through $(3,7)$ and $(5,4)?$

Put the coordinates into $y=mx+n$ and get $7=3m+n$ and $5=4m+n$.

Solve it and get $m=-1.5$ and $n=11.5,$ so the equation is $y=-1.5x+11.5$ or $3x+2y=23.\ _\square$

## Equation of Other Curves

The equation of conic sections are in the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$.

**Cite as:**2D Coordinate Geometry - Problem Solving.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/2d-coordinate-geometry-problem-solving/