Class 9 Mathematics β’ Ganita Manjari β’ Chapter 1
In this chapter, we learn how mathematics can be used to describe the exact position of a point. We use two number lines, called the x-axis and y-axis, to make a coordinate plane.
You will learn how to read coordinates, plot points, understand quadrants, find distances between points and solve coordinate-based problems.
Chapter concepts, explanations, examples and revision notes.
Important practice questions for examination preparation.
Exercise 1.1 ΰ€ΰ€° Exercise 1.2 ΰ€ΰ₯ questions, Hindi explanation ΰ€ΰ€° solutionsΰ₯€
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A coordinate plane is like a mathematical map. It helps us describe exactly where a point is located.
It is made using two number lines that cross each other at right angles.
Think of a coordinate plane like a map. Instead of saying "the point is near the school", we can give exact numbers to tell its position.
Coordinates are numbers used to tell us the position of a point on the coordinate plane.
Every coordinate pair has two numbers. The first tells us the horizontal position and the second tells us the vertical position.
Always read the x-coordinate first and the y-coordinate second.
A coordinate is written as an ordered pair.
The word "ordered" is important because the order of the numbers cannot be changed.
Consider:
and
These are two different points because the order of the numbers is different.
(2, 5) is NOT the same as (5, 2).
The horizontal line in a coordinate plane is called the x-axis.
It goes from left to right.
Horizontal = x-axis
On the x-axis, the y-coordinate is always zero.
The vertical line in a coordinate plane is called the y-axis.
It goes from bottom to top.
Vertical = y-axis
On the y-axis, the x-coordinate is always zero.
The point where the x-axis and y-axis meet is called the origin.
The origin is the starting point for plotting points on a coordinate plane.
Origin = Both coordinates are zero.
The first number in an ordered pair is called the x-coordinate.
The x-coordinate tells us how far the point is positioned horizontally from the y-axis.
For the point:
x-coordinate = 7
The second number in an ordered pair is called the y-coordinate.
The y-coordinate tells us the vertical position of a point relative to the x-axis.
For the point:
y-coordinate = 3
Plotting means marking a point at its correct position on the coordinate plane.
Start at (0, 0).
Move 4 units to the right.
Then move 3 units upward.
The final position is P(4, 3).
x first, y second.
When a point is already marked on a graph, we can find its coordinates by reading its horizontal and vertical position.
Suppose a point is 5 units to the right and 2 units upward from the origin.
Do not write (y, x). Always write (x, y).
The signs of the coordinates help us understand where a point is located.
| Coordinates | Position |
|---|---|
| (+, +) | Upper-right region |
| (-, +) | Upper-left region |
| (-, -) | Lower-left region |
| (+, -) | Lower-right region |
The sign of x tells the left/right direction and the sign of y tells the up/down direction.
The x-axis and y-axis divide the coordinate plane into four regions. These regions are called quadrants.
| Quadrant | x-coordinate | y-coordinate | Sign Pattern |
|---|---|---|---|
| First Quadrant | Positive | Positive | (+, +) |
| Second Quadrant | Negative | Positive | (-, +) |
| Third Quadrant | Negative | Negative | (-, -) |
| Fourth Quadrant | Positive | Negative | (+, -) |
Point A(4, 6) has both coordinates positive.
Therefore A lies in the First Quadrant.
Positive and negative numbers tell us the direction of a point from the axes.
| Coordinate | Meaning |
|---|---|
| Positive x | Move to the right |
| Negative x | Move to the left |
| Positive y | Move upward |
| Negative y | Move downward |
Move 4 units left and 3 units up.
Move 4 units right and 3 units down.
Coordinates can also help us find the distance between two points.
If two points have the same y-coordinate, subtract their x-coordinates and take the positive distance.
If two points have the same x-coordinate, use the difference between their y-coordinates.
For two general points, the distance can be found using the distance formula.
Let:
Both points have the same y-coordinate.
Therefore:
Always check whether the points lie on the same horizontal or vertical line before using the full distance formula.
Coordinates are not only used for graphs. They can also be used to solve real-life and geometry problems.
Suppose a school gate is represented by:
Because its y-coordinate is zero, the gate lies on the x-axis.
When solving a coordinate problem, first identify what each coordinate represents. Then use the signs, axes and distances carefully.
The midpoint is the point exactly halfway between two given points.
If:
Then:
Midpoint means the exact middle point of a line segment.
This chapter is based on the Class 9 Ganita Manjari Mathematics curriculum.
NCERT Ganita Manjari Textbook β CBSE Academic Curriculum 2026-27 β