Class 9 Notes - Coordinate Geometry

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1. Introduction to Coordinate Geometry

Coordinate Geometry (also called Cartesian Geometry) is the study of geometry using a coordinate system. It allows us to represent geometric shapes algebraically and solve geometric problems using equations.

2. Cartesian Plane

  • The Cartesian plane is formed by two perpendicular lines: the x-axis (horizontal) and the y-axis (vertical).
  • The point where they intersect is called the origin (O), with coordinates (0, 0).
  • The plane is divided into four quadrants.

3. Coordinates of a Point

  • Any point on the plane is represented by an ordered pair (x, y).
  • x-coordinate (abscissa): Distance from the y-axis.
  • y-coordinate (ordinate): Distance from the x-axis.
  • Example: The point (3, 2) is 3 units right of the y-axis and 2 units above the x-axis.

4. Plotting Points

  1. Start at the origin (0, 0).
  2. Move x units along the x-axis (right for positive, left for negative).
  3. From there, move y units parallel to the y-axis (up for positive, down for negative).
  4. Mark the point.
Example: Plot the point (-2, 4).
Move 2 units left and 4 units up from the origin.

5. Quadrants

  • Quadrant I: (+, +) — Both x and y are positive.
  • Quadrant II: (−, +) — x is negative, y is positive.
  • Quadrant III: (−, −) — Both x and y are negative.
  • Quadrant IV: (+, −) — x is positive, y is negative.

6. Applications

  • Locating positions on maps.
  • Describing the movement of objects.
  • Solving geometric problems algebraically.

7. Practice Questions

  1. Plot the points (2, 3), (−1, 4), (−3, −2), and (4, −3) on the Cartesian plane. Identify their quadrants.
  2. What are the coordinates of the origin?
  3. Which axis does the point (0, 5) lie on?
  4. Find the quadrant for the point (−5, −7).

8. Common Mistakes

  • Confusing the order of coordinates (x, y).
  • Plotting points in the wrong quadrant.
  • Forgetting to use negative signs for negative coordinates.

9. Summary

  • Coordinate geometry connects algebra and geometry.
  • Every point on the plane has unique coordinates (x, y).
  • The Cartesian plane is divided into four quadrants.
  • Plotting points correctly is the foundation for advanced geometry.