# Analytic geometry - One Dimensional Coordinate System

Point cordinates : $x_0,x_1,x_2,y_0,y_0,y_1,y_2$

Real number : $\lambda$

Distance Between two Points : d

1. Distance Between Twwo Points
$d=AB=|x_2-x_1|=|x_1-x_2|$

2. Dividing a Line Segment in the Ration $\lambda$
$x_0={ x_1+\lambda x_2 \over 1+ \lambda } , \lambda={AC \over CB }, \lambda \ne -1$

3. Midpoint of a Line Segment
$x_0= {x_1+x_2 \over 2}, \lambda=1 .$
One Dimensional Coordinate System Two Dimensional Coordinate System Straight Line in Plane Circle Ellipse Hyperbola Parabola Three Dimensional Coordinate System Plane Straight Line in Space Quadric Surfaces Sphere