Chapter 3: Coordinate Geometry

The Cartesian Plane

A Revolutionary Idea!

Developed by French mathematician René Descartes (1596-1650), the Cartesian plane lets us describe locations using numbers!


Building the Coordinate System

Step 1: Draw Two Perpendicular Lines

  • X-axis: Horizontal number line (→)
  • Y-axis: Vertical number line (↑)

Step 2: Mark the Origin

  • Origin (O): Where the axes meet = (0,0)(0, 0)

Step 3: Identify Directions

DirectionX valueY value
RightPositive (+)-
LeftNegative (-)-
Up-Positive (+)
Down-Negative (-)

The Four Quadrants

The axes divide the plane into 4 regions:

QuadrantPositionCoordinates
ITop-Right(+,+)(+, +)
IITop-Left(,+)(-, +)
IIIBottom-Left(,)(-, -)
IVBottom-Right(+,)(+, -)

Memory Trick: Start from Quadrant I (positive area) and go counter-clockwise!


Why is This Useful?

With coordinates, we can:

  • Describe exact locations
  • Plot shapes using equations
  • Calculate distances between points
  • Analyze geometric relationships
Visualizer
Coordinate Plane
XYOA(3, 4)B(-2, 3)C(-3, -2)D(4, -1)Q I (+,+)Q II (-,+)Q III (-,-)Q IV (+,-)
Point A: (3, 4)
Quadrant I

Interactive Visualization