Math 101

Intermediate Algebra 

The Cartesian Coordinate System
Chapter 3, Section 1

Cartesian CoordinatesOverview


 Locate points in 2D by specifying where the point is relative to the Origin.
 Any point may be specified by an ordered pair (described below).
 The horizontal line labeled "x" is the xaxis.
 The vertical line labeled "y" is the yaxis.
 Quadrants are regions of the plane relative to the origin.
 Quadrant I: x > 0 and y > 0
 Quadrant II: x < 0 and y > 0
 Quadrant III: x < 0 and y < 0
 Quadrant IV: x > 0 and y < 0


Ordered Pairs (x, y)


 Any point in 2D may be located by an ordered pair (x, y).
 The xcoordinate, x, is the value on the xaxis vertically above or below the point.
 The ycoordinate, y, is the value on the yaxis horizontally right or left of the point.
 The order is that the xcoordinate is listed first and the ycoordinate is listed second.


Distance Formula


The distance formula gives the distance, d, between 2 given points
(x_{1}, y_{1})
and (x_{2}, y_{2}).
Distance is always nonnegative.


Midpoint Formula


The midpoint formula gives an ordered pair that is the point halfway between 2 given points
(x_{1}, y_{1})
and (x_{2}, y_{2}).
