Calculating Distance Between Two Points on a Coordinate Plane: The Comprehensive Guide

Distance formula

The distance formula is a mathematical equation that allows you to calculate the distance between two points in a coordinate plane

The distance formula is a mathematical equation that allows you to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the context of two points (x₁, y₁) and (x₂, y₂) on a coordinate plane, the distance formula can be expressed as:

d = √((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 call them (x₁, y₁) and (x₂, y₂).

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

3. Square the result of step 2: (x₂ – x₁)².

4. Repeat steps 2 and 3 for the y-coordinates: (y₂ – y₁) and (y₂ – y₁)².

5. Add the squared x-coordinate difference and squared y-coordinate difference together: (x₂ – x₁)² + (y₂ – y₁)².

6. Finally, take the square root of the result from step 5 to find the distance: d = √((x₂ – x₁)² + (y₂ – y₁)²).

By following these steps, you can successfully find the distance between any two points on a coordinate plane using the distance formula.

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