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# Cartesian Coordinate System – Example, Formulas

## Introduction

The Cartesian coordinate system is an essential tool in geometry that allows us to locate points in a two-dimensional space using two perpendicular number lines. In this article, we will explore the basics of the Cartesian coordinate system and how it can be used in geometry.

## What is the Cartesian Coordinate System?

The Cartesian coordinate system, also known as the rectangular coordinate system. It is a mathematical system that uses two perpendicular number lines, the x-axis and the y-axis, to define a point in a two-dimensional space. The x-axis is a horizontal line, and the y-axis is a vertical line that intersect at the origin (0, 0).

## Understanding the Axes

The x-axis is used to measure the horizontal distance of a point from the origin, and the y-axis is used to measure the vertical distance of a point from the origin. The distance of a point from the origin is called its coordinates. It is denoted by (x, y). The x-coordinate is the horizontal distance from the origin, and the y-coordinate is the vertical distance from the origin.

## Plotting Points

1. To plot a point in the Cartesian coordinate system, we start at the origin.
2. After that move horizontally to the right if the x-coordinate is positive or to the left if the x-coordinate is negative.
3. Then we move vertically up if the y-coordinate is positive or down if the y-coordinate is negative until we reach the point.

### The Distance Formula

The distance between two points in the Cartesian coordinate system can be found using the distance formula, which is:

d = sqrt[(x2 – x1)^2 + (y2 – y1)^2]

where (x1, y1) and (x2, y2) are the coordinates of the two points.

☛Related Topics

The following topic would be helpful in better understanding of the cartesian coordinate system.

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