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Coordinate Geometry

Class 9 Maths • Chapter 03 • Comprehensive Guide

1. The Cartesian System

Coordinate Geometry helps us locate a point in a plane using two perpendicular reference lines. This system was developed by the French mathematician Rene Descartes.

X X' Y Y' O(0,0) I II III IV
Key Definitions
  • Origin (O): The point where the X-axis and Y-axis intersect. Coordinates: \( (0, 0) \).
  • X-axis: The horizontal number line (\( X'OX \)).
  • Y-axis: The vertical number line (\( Y'OY \)).
Solve Exercise 3.1 (Cartesian System)

2. Quadrants & Sign Convention

The axes divide the plane into four parts called Quadrants. The sign of coordinates depends on the quadrant.

Quadrant X-coordinate Y-coordinate Sign
I (First) Positive (+) Positive (+) \((+, +)\)
II (Second) Negative (-) Positive (+) \((-, +)\)
III (Third) Negative (-) Negative (-) \((-, -)\)
IV (Fourth) Positive (+) Negative (-) \((+, -)\)

2.1 Quadrant Logic (No Memorizing)

Just ask two questions:

(+, +) -> Quadrant I
(-, +) -> Quadrant II
(-, -) -> Quadrant III
(+, -) -> Quadrant IV

Trick

Move anticlockwise starting from (+,+).

Quadrant Hunter

Enter coordinates to find their home!

Waiting for input...

3. Understanding Coordinates

The position of a point is given by an ordered pair \( (x, y) \).

Term Alternative Name Definition
x-coordinate Abscissa Perpendicular distance from the Y-axis.
y-coordinate Ordinate Perpendicular distance from the X-axis.
Watch Out:
The coordinates \( (x, y) \) are NOT the same as \( (y, x) \) unless \( x = y \). That's why they are called "ordered pairs".

3.1 Why Are Coordinates Ordered?

Imagine this: You tell a friend your seat location.

Row 3, Seat 5 is NOT the same as Row 5, Seat 3.

Similarly:

Warning: CBSE Trap: Swapping coordinates gives a different point!
Think

Can two different ordered pairs represent the same point?

No. Order matters.

3.2 How to Plot a Point (CBSE Method)

To plot a point \( (x, y) \):

  1. Start from the origin (0,0)
  2. Move x units along X-axis (right if +, left if -)
  3. From there, move y units parallel to Y-axis
  4. Mark the point and label it
Exam Tip

CBSE awards marks for correct steps even if the point is slightly misplaced.

4. Points on the Axes

What if a point lies exactly on a line?

Point on X-axis

If a point is on the X-axis, its distance from the X-axis is zero.

Therefore, its y-coordinate (ordinate) is 0.

Form: \( (x, 0) \)

Point on Y-axis

If a point is on the Y-axis, its distance from the Y-axis is zero.

Therefore, its x-coordinate (abscissa) is 0.

Form: \( (0, y) \)

4.1 Distance from Axes - Think Visually

Key Idea:

Example: Point \( P(-4, 3) \)

Warning: Sign does NOT affect distance, only magnitude matters.

Coordinates in Real Life

Coordinate geometry helps computers, GPS, and games understand where things are.

🏆 NCERT Exemplar (Advanced)

Targeting full marks? Solve these higher-level problems from NCERT Exemplar.

3.1 MCQs 3.2 Short Ans 3.3 Short Ans 3.4 Long Ans

Exam Smart Zone

Common board-style questions. Click to reveal simplified solutions.

Q1: In which quadrant does the point (-3, 5) lie?

Solution: x = -3 (negative), y = 5 (positive)

(-, +) -> Quadrant II

Q2: Write the coordinates of a point on the X-axis at a distance of 4 units to the left of origin.

Solution: On the X-axis, y = 0.

Left of origin means x is negative.

Therefore Point = (-4, 0)

Q3: Find the perpendicular distance of point P(3, 4) from the X-axis and Y-axis.

Distance from X-axis = |y-coordinate| = |4| = 4 units

Distance from Y-axis = |x-coordinate| = |3| = 3 units

Q4: Plot the points A(2, 3), B(-1, 2), C(-3, -4), D(4, -1) and identify their quadrants.

A(2, 3): (+, +) -> Quadrant I

B(-1, 2): (-, +) -> Quadrant II

C(-3, -4): (-, -) -> Quadrant III

D(4, -1): (+, -) -> Quadrant IV

Common CBSE Mistakes

Avoid these -> Easy marks saved.

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