AI draft — not yet reviewed by a teacher. Check with your teacher.

Mathematics · Class 9 · Chapter 16: Introduction to Coordinate Geometry

8 min

Key points

Coordinate geometry is a branch of mathematics which deals with the study of geometry using coordinates
The coordinate system consists of two perpendicular lines called axes - horizontal axis (x-axis) and vertical axis (y-axis)
The point of intersection of x-axis and y-axis is called the origin, denoted by O(0,0)
Any point in the plane is represented by an ordered pair (x,y) where x is abscissa and y is ordinate
The coordinate axes divide the plane into four parts called quadrants - I, II, III, and IV
Distance between two points A(x₁,y₁) and B(x₂,y₂) is given by d = √[(x₂-x₁)² + (y₂-y₁)²]
Mid-point of line segment joining points A(x₁,y₁) and B(x₂,y₂) is ((x₁+x₂)/2, (y₁+y₂)/2)
Section formula divides a line segment internally in the ratio m:n

Definitions

Coordinate Geometry: Coordinate geometry is a branch of mathematics which deals with the study of geometry using coordinates.
Abscissa: The x-coordinate of a point is called its abscissa.
Ordinate: The y-coordinate of a point is called its ordinate.
Origin: The point of intersection of coordinate axes is called the origin.
Quadrant: The coordinate axes divide the plane into four parts called quadrants.

Worked example

Define coordinate axes and identify the coordinates of point P shown in the given figure where P is located 3 units right and 2 units up from origin. (5 marks)

Coordinate axes are two perpendicular number lines that intersect at a point called origin. The horizontal line is called x-axis and vertical line is called y-axis. The coordinates of point P are (3, 2) where 3 is the abscissa and 2 is the ordinate.

Common mistakes

Students often confuse abscissa with ordinate - remember x comes first, then y
Always write the distance formula before solving distance problems
Students forget to take square root in distance formula
Wrong signs in quadrants - remember ASTC rule for signs
Not simplifying coordinates properly in mid-point calculations

Quick recap

Coordinate geometry uses two perpendicular number lines (coordinate axes) intersecting at origin to locate points. X-axis is horizontal, Y-axis is vertical. Every point has coordinates (x, y) where x is abscissa and y is ordinate. The plane is divided into four quadrants with different sign combinations.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.