How to Find the Distance Between Coordinates in Cartesian System

What is a Coordinate System?

A coordinate system is a system used to define the position of points in space. It is used in mathematics, engineering, and science to describe the location of an object. The most common type of coordinate system is the Cartesian coordinate system, which is a rectangular coordinate system that uses an x-axis, y-axis, and z-axis to describe the position of a point. In this system, each point is represented by a set of numbers, which represent the distance of the point from the origin of the system.

How to Find the Distance Between Coordinates

To find the distance between two points in a Cartesian coordinate system, you need to use the Pythagorean theorem. This theorem states that the square of the hypotenuse of a right triangle (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, it states that the distance between two points is equal to the square root of the sum of the squares of the differences between the two points' x-coordinates and y-coordinates.

For example, to find the distance between the two points (2, 3) and (4, 5), you would first find the differences between the two points' x-coordinates and y-coordinates. In this case, the difference between the x-coordinates is 2 (4 - 2 = 2) and the difference between the y-coordinates is 2 (5 - 3 = 2).

To calculate the distance, you would then take the square root of the sum of the squares of the differences. In this example, the distance is equal to the square root of 8, which is equal to 2.8284.

Conclusion

By using the Pythagorean theorem, you can easily find the distance between two points in a Cartesian coordinate system. All you need to do is calculate the differences between the two points' x-coordinates and y-coordinates, and then take the square root of the sum of the squares of the differences.