Coordinate Geometry Notes Class 9
Coordinate Geometry, also known as Analytical Geometry or Cartesian Geometry, is one of the most important topics in mathematics. It connects two major branches, i.e., Algebra and Geometry. It allows geometric shapes to be expressed in numerical and algebraic form. Before the development of this field, geometry was purely visual, based on drawings and reasoning about shapes. However, coordinate geometry introduced a new way to solve geometric problems using equations and numbers.
By assigning each point on a surface a unique pair of numbers, called coordinates, mathematicians can describe exact positions and calculate various properties like distance, area, slope, and midpoint.
Introduction to the Cartesian System
The fundamental tool in coordinate geometry is the Cartesian coordinate system. It was developed by René Descartes. This system allows us to locate any point in a two-dimensional plane using two perpendicular lines, called axes.
- X-axis (Horizontal): This is the horizontal number line, where positions are measured left and right. It is also referred to as the Abscissa axis.
- Y-axis (Vertical): This is the vertical number line, where positions are measured up and down. It is also referred to as the Ordinate axis.
The point where the X-axis and Y-axis intersect is called the Origin, and its coordinates are always (0, 0).
The Coordinates of a Point
Every point on the plane is uniquely identified by an ordered pair of numbers, called its coordinates, written as (x, y).
- The first number, x, represents the position along the X-axis (the horizontal distance from the Y-axis).
- The second number, y, represents the position along the Y-axis (the vertical distance from the X-axis).
Quadrants and Sign Conventions
The two axes divide the entire plane into four regions known as Quadrants. These quadrants are numbered I, II, III, and IV in a counter-clockwise direction, starting from the upper-right section. Understanding the sign conventions in each quadrant is crucial for plotting.
| Quadrant | X-coordinate Sign | Y-coordinate Sign | Example Point |
|---|---|---|---|
| I | Positive (+) | Positive (+) | (3, 5) |
| II | Negative (-) | Positive (+) | (-2, 4) |
| III | Negative (-) | Negative (-) | (-6, -1) |
| IV | Positive (+) | Negative (-) | (7, -3) |
Plotting Points on the Plane
The main skill learned in Class 9 coordinate geometry is accurately plotting points given their coordinates.
To locate a point (x, y):
- Start at the Origin (0, 0).
- Move horizontally according to x. If x is positive, move right; if x is negative, move left.
- From that new horizontal position, move vertically according to y. If y is positive, move up; if y is negative, move down. The final location is the point (x, y).
Points on the Axes:
- Any point that lies on the X-axis will have a y-coordinate of 0 (e.g., (5, 0)).
- Any point that lies on the Y-axis will have an x-coordinate of 0 (e.g., (0, -4)).
