Coordinate Geometry

Class 10 Mathematics • Chapter 7

Chapter Overview

Coordinate Geometry provides a way to study geometry using numbers, coordinates and algebra.

In this chapter, students learn how to calculate distances between points, locate a point dividing a line segment in a given ratio, and determine the area of a triangle using coordinates.

The chapter also develops the connection between geometric figures and algebraic calculations.

📘 Complete Notes

Definitions, coordinate plane, formulas, solved examples, important concepts and revision notes.

❓ Important Questions

Conceptual, formula-based, reasoning and exam-oriented practice questions.

📝 Exercises

Complete exercise questions with step-by-step solutions, diagrams and Hindi explanations.

🔢 Numericals

Distance formula, section formula, area and coordinate-based numerical problems.

🎯 Practice Zone

Extra practice problems, mixed questions and quick coordinate challenges.

Topics Covered

Cartesian Coordinate Plane

Coordinates of a Point

x-axis and y-axis

Quadrants

Distance Between Two Points

Distance Formula

Section Formula

Internal Division of a Line Segment

Midpoint Formula

Ratio and Coordinates

Area of a Triangle

Collinearity of Points

Coordinate-Based Geometry

Geometrical Interpretation

Applications of Coordinate Geometry

⭐ Key Formulas to Remember

Distance Formula

Distance between (x₁, y₁) and (x₂, y₂):

√[(x₂ − x₁)² + (y₂ − y₁)²]

Section Formula

If P divides the line segment joining (x₁, y₁) and (x₂, y₂) internally in the ratio m : n, then

P = ( (mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n) )

Midpoint Formula

Midpoint of (x₁, y₁) and (x₂, y₂):

( (x₁ + x₂)/2, (y₁ + y₂)/2 )

Area of Triangle

For points (x₁, y₁), (x₂, y₂), (x₃, y₃):

Area = 1/2 | x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) |

💡 Key Results to Remember

The x-coordinate is called the abscissa.
The y-coordinate is called the ordinate.
Points on the x-axis have y-coordinate equal to 0.
Points on the y-axis have x-coordinate equal to 0.
The origin is represented by (0, 0).
The distance formula is based on the Pythagorean theorem.
The midpoint divides a line segment into two equal parts.
Section formula gives the coordinates of a point dividing a line segment in a specified ratio.
Area of a triangle can be calculated directly from the coordinates of its three vertices.
Three points are collinear when the area of the triangle formed by them is zero.

⚡ Quick Revision

Coordinate
(x, y)

Origin
(0, 0)

x-axis
y = 0

y-axis
x = 0

Distance
√[(x₂−x₁)²+(y₂−y₁)²]

Midpoint
((x₁+x₂)/2, (y₁+y₂)/2)

Section Formula
Internal division in m:n

Triangle Area
Coordinate determinant formula

Collinearity
Triangle area = 0

📚 Recommended Study Order

Start with the coordinate plane and understand how points are represented. Then learn the Distance Formula and practise numerical questions. After that, study the Section Formula and Midpoint Formula. Finally, practise Area of Triangle and Collinearity problems.

📘 Start Notes ❓ Important Questions 📝 Exercises 🔢 Numericals

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