## Distance Formula

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

The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. It can be applied in both two-dimensional (2D) and three-dimensional (3D) spaces.

In 2D, let’s consider two points A(x1, y1) and B(x2, y2). The distance between points A and B can be calculated using the formula:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

Here, “d” represents the distance between point A and point B, and sqrt refers to the square root. The formula takes the difference between the x-coordinates and squares it, adds it to the squared difference between the y-coordinates, and then calculates the square root of the sum.

For example, if point A is (2, 3) and point B is (5, 7), the distance would be:

d = sqrt((5 – 2)^2 + (7 – 3)^2)

= sqrt(3^2 + 4^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

Therefore, the distance between points A and B is 5 units.

In 3D, the distance formula follows a similar concept, but with an additional z-coordinate. Given two points A(x1, y1, z1) and B(x2, y2, z2), the distance formula becomes:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

Here, “d” represents the distance between point A and point B. The formula calculates the difference between the x-coordinates and squares it, adds it to the squared difference between the y-coordinates, and also adds the squared difference between the z-coordinates. Finally, it takes the square root of the sum.

Understanding and applying the distance formula is important in various mathematical concepts, like geometry, physics, and even computing the shortest paths in graphs. It allows us to measure the distance between points accurately in any coordinate space.

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