Calculate Distances Between Points Using the Distance Formula in Mathematics

Distance Formula

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

The distance formula is a mathematical formula used to calculate the distance between two points in a coordinate plane. It is applicable in both two-dimensional (x, y) and three-dimensional (x, y, z) coordinate systems.

In a two-dimensional coordinate system, let’s consider two points with coordinates (x1, y1) and (x2, y2). The distance formula between these two points can be stated as:

d = √((x2-x1)^2 + (y2-y1)^2)

In a three-dimensional coordinate system, the formula becomes:

d = √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

To use the distance formula, follow these steps:

1. Identify the coordinates of the two points (x1, y1, z1) and (x2, y2, z2).
2. Substitute the values into the distance formula.
3. Simplify the expression by subtracting the respective components and squaring the differences.
4. Add up the squares.
5. Take the square root of the sum to find the distance between the two points.

For example, suppose we have two points A(2, 3) and B(5, 1) in a two-dimensional coordinate system. We can find the distance between these two points using the distance formula:

d = √((5-2)^2 + (1-3)^2)
= √(3^2 + (-2)^2)
= √(9 + 4)
= √13

Hence, the distance between points A and B is √13.

It’s essential to remember that the distance formula only provides the magnitude of the distance between points, not the direction. To account for direction, you may need additional information or calculations.

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