# Coordinate Geometry

Within a Cartesian Coordinate System, each point in space has an π₯ β πππππππππ‘π and a π¦ β πππππππππ‘π representing its horizontal position and vertical position. The coordinates are written as an ordered pair, (π₯, π¦).

## 1. Distance Formula

The length of a line joining two points can be found based on the Pythagorean Theorem.

AB=\sqrt{(x_2-x_1 )^2+(y_2-y_1 )^2}

## 2. Midpoint Formula

The midpoint of a line joining two points, Β is given by:

M=[\frac{1}{2} (x_2-x_1 ),\frac{1}{2} (y_2-y_1 )]

## 3. Slope of a Line

The slope of a line is the measure of its gradient at any given point. Β could stand for βmodulus of slope.β β the reason is unknown*

Slope,m^*=\frac{Ξy}{Ξx}

Positive Slope (m>0)

Gradient = tan\theta

Negative Slope (m<0)

\beta is an obtuse angle with the positive sense of the x-axis.

Gradient = tan\theta

## 4. Parallel Lines

## 5. Perpendicular Lines

If l_1 and l_2 are perpendicular their slopes must be negative reciprocals of each other:

m_1=-\frac{1}{m_2} OR m_1 m_2=-1