📝 Chapter Notes & Revision

Coordinate Geometry

🏫 MP BoardClass 9Mathematics

📐 Formula & Cheat Sheet (English)

Quick Revision Notes: Coordinate Geometry

Class: 9th Mathematics (MP Board)
Subject: Coordinate Geometry (निर्देशांक ज्यामिति)

Introduction to Coordinate Geometry

  • Coordinate Geometry: It is a branch of mathematics in which geometric figures are studied using algebra (coordinate systems).
  • René Descartes: The system of describing the position of a point in a plane was developed by the French mathematician René Descartes.

Key Terms & Definitions

  1. Cartesian System (कार्तीय पद्धति): To locate the position of a point on a plane, we require two perpendicular number lines:

    • Horizontal Line: Called the X-axis (XOX').
    • Vertical Line: Called the Y-axis (YOY').
    • Origin (मूल बिंदु): The point of intersection of the X-axis and Y-axis. It is denoted by O and its coordinates are (0, 0).

  2. Axes (अक्ष): Together, the X-axis and Y-axis are called the coordinate axes (निर्देशांक अक्ष).

  3. Quadrants (चतुर्थांश): The two axes divide the plane into four parts called quadrants. They are numbered counter-clockwise starting from the top-right:

    • 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.

Coordinates of a Point (बिंदु के निर्देशांक)

  • The position of any point P in a Cartesian plane is represented by an ordered pair (x, y).
  • Abscissa (भुज): The x-coordinate of a point. It is the perpendicular distance of the point from the Y-axis.
  • Ordinate (कोटिक): The y-coordinate of a point. It is the perpendicular distance of the point from the X-axis.

Note: If a point is on the X-axis, its y-coordinate is always 0 (x, 0).
If a point is on the Y-axis, its x-coordinate is always 0 (0, y).

Sign Convention Summary (चिन्ह परिपाटी)

QuadrantX-coordinateY-coordinateCoordinate Sign (x, y)
Quadrant IPositive (+)Positive (+)(+, +)
Quadrant IINegative (-)Positive (+)(-, +)
Quadrant IIINegative (-)Negative (-)(-, -)
Quadrant IVPositive (+)Negative (-)(+, -)

Important Tips for MP Board Exam Preparation

  1. Always draw arrows on the axes (XOX' and YOY') and label the Origin O.
  2. Maintain equal units/divisions on both the X-axis and Y-axis while plotting graphs.
  3. While writing coordinates, always write the x-coordinate first, followed by a comma, and then the y-coordinate inside parentheses, e.g., (3, -4).
  4. Questions commonly asked:
    • Identifying the quadrant in which a given point lies.
    • Writing the abscissa or ordinate of a given point.
    • Plotting points on the Cartesian plane.