Class 9 Maths – Coordinate Geometry

Class 9 Maths – Coordinate Geometry

3.1 Introduction

Coordinate Geometry studies the position of points on a plane using numbers.
Each point is represented by an ordered pair (x, y) called its coordinates.
The x-coordinate is called the abscissa, and the y-coordinate is called the ordinate.

Uses:

Locating points on a plane
Finding distance between points
Determining the midpoint of a line segment

3.2 Cartesian System

Introduced by René Descartes, hence called Cartesian coordinate system.
It consists of:
1. Two perpendicular axes:
  - x-axis (horizontal)
  - y-axis (vertical)
2. Origin: Point of intersection of x-axis and y-axis (0, 0).
3. Quadrants:
  - I: (+, +)
  - II: (−, +)
  - III: (−, −)
  - IV: (+, −)

Plotting a Point

Start at the origin (0, 0).
Move along the x-axis to reach x-coordinate.
Move parallel to y-axis to reach y-coordinate.
Mark the point.

Distance Formula (Optional Extension)

For points A(x₁, y₁) and B(x₂, y₂): $\text{Distance} = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$ Distance=(x2−x1)2+(y2−y1)2

Midpoint Formula (Optional Extension)

Midpoint of AB: $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ M=(2×1+x2,2y1+y2)

3.3 Summary

Coordinate system helps in locating points on a plane.
Each point is represented by (x, y).
Quadrants divide the plane into four parts.
Distance and midpoint formulas are useful in geometry problems.

Quick Short Q&A (Most Possible)

Question	Short Answer
What is coordinate geometry?	Study of points on a plane using coordinates
Coordinates of origin?	(0, 0)
x-coordinate called?	Abscissa
y-coordinate called?	Ordinate
Quadrants in plane?	I, II, III, IV
Sign of coordinates in Quadrant II?	(−, +)
How to plot a point (x, y)?	Move x along x-axis, then y along y-axis
Distance formula between (x₁, y₁) & (x₂, y₂)?	√((x₂−x₁)² + (y₂−y₁)²)
Midpoint formula?	((x₁+x₂)/2, (y₁+y₂)/2)
Who introduced Cartesian system?	René Descartes