How to Use the Distance Formula to Calculate the Distance Between Two Points in a Coordinate Plane

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 derived from the Pythagorean theorem.

In a two-dimensional Cartesian coordinate system, let’s say we have two points, (x1, y1) and (x2, y2). The distance between these two points can be found using the following formula:

d = √((x2 – x1)^2 + (y2 – y1)^2)

The formula calculates the length of the line segment connecting the two points.

To use the distance formula, follow these steps:

1. Identify the coordinates of the two points you want to find the distance between.
2. Assign the values of x1, y1, x2, and y2 in the distance formula.
3. Substitute these values into the formula and perform the operations according to the order of operations (PEMDAS/BODMAS) to simplify the equation.
4. Finally, take the square root (√) of the simplified equation to get the distance (d) between the two points.

Here’s an example to better illustrate how to use the formula:

Let’s find the distance between the points (2, 4) and (6, 8).

Using the distance formula:

d = √((6 – 2)^2 + (8 – 4)^2)
= √((4)^2 + (4)^2)
= √(16 + 16)
= √(32)
≈ 5.66 (rounded to two decimal places)

Therefore, the distance between the points (2, 4) and (6, 8) is approximately 5.66 units.

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