## distance formula

### The distance formula is used to find the distance between two points in a coordinate plane

The distance formula is used to find the distance between two points in a coordinate plane. It is also known as the Euclidean distance, named after the ancient Greek mathematician Euclid.

In a two-dimensional plane, let’s say we have two points (x1, y1) and (x2, y2). The distance formula states that the distance between these two points is given by:

√((x2 – x1)^2 + (y2 – y1)^2)

To understand the formula better, let’s break it down:

1. Subtract the x-coordinates of the two points: (x2 – x1). This gives the difference in the horizontal direction between the two points.

2. Square the difference obtained in step 1: (x2 – x1)^2.

3. Subtract the y-coordinates of the two points: (y2 – y1). This gives the difference in the vertical direction between the two points.

4. Square the difference obtained in step 3: (y2 – y1)^2.

5. Add the squared results from steps 2 and 4: (x2 – x1)^2 + (y2 – y1)^2.

6. Take the square root of the sum obtained in step 5: √((x2 – x1)^2 + (y2 – y1)^2).

This gives you the distance between the two points, which is always a positive value or zero.

The distance formula can also be extended to three-dimensional space by adding the z-coordinate difference, and so on for higher dimensions.

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