Mastering the Distance Formula | A Comprehensive Guide to Calculating Distances between Points in a Coordinate Plane

Distance Formula

The distance formula is a mathematical equation that calculates the distance between two points in a coordinate plane

The distance formula is a mathematical equation that calculates the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

The distance formula is as follows:

Given two points in a coordinate plane: (x₁, y₁) and (x₂, y₂), the distance between these points can be found using the formula:

Distance = √((x₂ – x₁)² + (y₂ – y₁)²)

Here’s a step-by-step breakdown of how to use the distance formula:

1. Identify the coordinates of the two points you want to find the distance between. Let’s say the first point is (x₁, y₁) and the second point is (x₂, y₂).

2. Calculate the difference between the x-coordinates of the two points. Subtract x₁ from x₂: (x₂ – x₁).

3. Calculate the difference between the y-coordinates of the two points. Subtract y₁ from y₂: (y₂ – y₁).

4. Square the result from step 2: (x₂ – x₁)².

5. Square the result from step 3: (y₂ – y₁)².

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

7. Take the square root of the sum from step 6: √((x₂ – x₁)² + (y₂ – y₁)²).

The result will give you the distance between the two points in the coordinate plane.

Note: The distance formula can be used in multiple dimensions, not just on a 2D plane. The concept remains the same, but the formula becomes more complex with additional variables for each dimension.

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