Co-Ordinate Geometry

Co-Ordinate Geometry

1. Definition

   • Coordinate Geometry describes the link between geometry and algebra through graphs involving curves and lines. It is a part of geometry where the position of points on the plane is described using an ordered pair of numbers.

2. Requirement: Two perpendicular lines

   • Horizontal line: x axis
   • Vertical line : y axis

3. Cartesian System

   • Used for: Describing the position of a point in a plane
   • Developed by : Renes Descartes a french mathematician
   • Denoted by : (x,y)
     • x coordinate is abscissa
     • y coordinate is ordinate
   • Divided in: 4 quadrants
     • Quadrant I : (x,y)
     • Quadrant II : (-x, y)
     • Quadrant III : (-x, -y)
     • Quadrant IV : (x, -y)

4. Graph - Linear Equation

   • Step 1: Convert given equation in the form y = mx + c
   • Step 2: Select at least 3 values of x, such that x, y ∈ l
   • Step 3: Draw the table for ordered pair (x,y)
   • Step 4: Plot these ordered points on the graph paper
   • Step 5: Draw a straight line passing through plotted points

5. Fixed Point: Is the origin (0, 0) where x axis and y axis meet

   • Moving left: -ve x axis (-x, 0)
   • Moving right: +ve x axis (x,0)
   • Moving up: +ve y axis (0,y)
   • Moving down: -ve y axis (0, -y)

6. Plotting point in a plane (5,4)

   • Step 1: Draw co-ordinate axis and select units
     • Step 2: Starting from origin, count units on x and y axis
       • Step 3: Mark the corresponding points

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