---
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id: "69f869a8293c3123114da10a"
title: "Coordinate Geometry"
board: "CBSE"
curriculum: "CBSE"
class: "Class 10"
subject: "Mathematics"
book: "Mathematics"
chapter: "Coordinate Geometry"
chapter_slug: "coordinate-geometry"
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---

# Coordinate Geometry
In this chapter on Coordinate Geometry, you will learn about the position of points on a plane using coordinate axes, the concept of coordinates (abscissa and ordinate), and the application of the distance formula. The chapter concludes with discussions on the section formula to find specific points dividing line segments in given ratios.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Coordinate Geometry |
| Pages | 99-112 |

---

## Chapter Summary

### Short Summary
This chapter explains how to locate points on a plane using coordinates, introduces the distance formula for calculating distances between points, and discusses the section formula for determining a point that divides a line segment in a specific ratio.

### Detailed Summary
In Class IX, it was established that a point's position on a plane is determined by its coordinates—its distance from the x-axis (ordinate) and y-axis (abscissa). The distance formula is developed to find distances between two points based on their coordinates. You can apply the Pythagorean theorem for various scenarios, including points aligned on the x-axis, y-axis, or in different quadrants. The chapter also discusses finding specific coordinates that maintain equal distances from two points, along with practical examples to understand triangle formation through coordinates.

---

## Topic-Wise Explanation

### Introduction to Coordinate Geometry
The topic introduces the coordinate axes and how to represent points in a plane using coordinates.

### Distance Formula
The distance formula for two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is derived using the Pythagorean theorem: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$. Special cases for points on the axes are also mentioned.

### Section Formula
This section covers how to find the coordinates of a point that divides the line segment joining two given points in a specific ratio.

### Summary of Key Concepts
Key concepts from the chapter include the definitions and applications of the distance formula and section formula in solving practical problems in coordinate geometry.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Coordinate Axes | The framework to locate any point on a plane using x and y coordinates. |
| Distance Formula | A mathematical formula used to calculate the distance between two points in a plane. |
| Section Formula | A formula to determine the coordinates of a point that divides a segment into a certain ratio. |

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## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Abscissa | The x-coordinate of a point; the horizontal distance from the y-axis. |
| Ordinate | The y-coordinate of a point; the vertical distance from the x-axis. |
| Pythagorean Theorem | A fundamental relation in Euclidean geometry among the three sides of a right triangle. |

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## Important Points for Revision

* Coordinate axes are essential for positioning points in a plane.
* The distance between two points can be easily computed using the distance formula.
* The section formula enables finding points that divide a segment in a specific ratio.
* Practical applications of coordinate geometry are significant in fields like physics and engineering.
* Understanding key terms like abscissa and ordinate is crucial.
* The distance formula can simplify complex geometric problems.
* Graphs of linear equations represent straight lines in coordinate geometry.
* Quadratic functions represent parabolas and can be analyzed using coordinates.

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## Practice Questions

### Short Answer Questions
1. Explain the terms abscissa and ordinate.
2. How would you find the distance between points $(4,0)$ and $(6,0)$?
3. State the distance formula.
4. What is the significance of the section formula?
5. Can you determine coordinates of a point given the ratio it divides a segment?

### Long Answer Questions
1. Derive the distance formula using the Pythagorean theorem. Provide an example.
2. Explain how to determine if three given points form a triangle using the distance formula.
3. Describe the section formula and its application with an example.

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69f869a8293c3123114da10a |
| Canonical URL | https://www.edzy.ai/cbse-class-10-mathematics-coordinate-geometry |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-10-mathematics-coordinate-geometry.md |