# 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.

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