Calculating Distance between Two Points in a Coordinate Plane: The Distance Formula Explained with Examples

Distance formula

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

The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem.

The formula is as follows:
Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2)

Where:
– sqrt refers to the square root function
– (x1, y1) and (x2, y2) are the coordinates of the two points in the plane

To use the distance formula, follow these steps:

1. Identify the coordinates of the two points. Let’s say we have point A with coordinates (x1, y1) and point B with coordinates (x2, y2).

2. Plug the coordinates into the distance formula.
Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2)

3. Subtract the x-coordinates and square the result: (x2 – x1)^2
This represents the difference in the x-values of the two points, squared.

4. Subtract the y-coordinates and square the result: (y2 – y1)^2
This represents the difference in the y-values of the two points, squared.

5. Add the results from step 3 and step 4 together.

6. Finally, take the square root of the sum obtained in step 5 to find the distance between the two points.

Let’s consider an example to understand this better:
Suppose we have two points, A with coordinates (2, 4) and B with coordinates (6, 8).

Using the distance formula:
Distance = sqrt((6 – 2)^2 + (8 – 4)^2)
= sqrt(4^2 + 4^2)
= sqrt(16 + 16)
= sqrt(32)
= 5.66 (approximately)

So, the distance between points A and B is approximately 5.66 units.

The distance formula can be applied in various situations, such as measuring distances between cities on a map, finding the length of a diagonal in a rectangle, or determining the distance between any two points in a coordinate plane.

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