Calculating Distance Between Two Points: The Distance Formula Explained with Step-by-Step Instructions and Example

Distance Formula

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

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

Let’s consider two points in the coordinate plane: (x1, y1) and (x2, y2). The distance (d) between these two points can be calculated using the distance formula:

d = √[(x2 – x1)^2 + (y2 – y1)^2]

Here’s a step-by-step explanation 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 we have point A at (x1, y1) and point B at (x2, y2).

2. Substitute the x and y coordinates into the distance formula:

d = √[(x2 – x1)^2 + (y2 – y1)^2]

3. Calculate the differences between the x-coordinates and the y-coordinates:

x2 – x1 = Δx
y2 – y1 = Δy

4. Square the differences:

(Δx)^2 = (x2 – x1)^2
(Δy)^2 = (y2 – y1)^2

5. Sum the squared differences:

[(x2 – x1)^2 + (y2 – y1)^2]

6. Take the square root of the sum:

d = √[(x2 – x1)^2 + (y2 – y1)^2]

After going through these steps, you will have found the distance between the two points.

Let’s take an example to illustrate this:

Consider two points A(3, 4) and B(7, 8). To find the distance between these two points, we will use the distance formula:

d = √[(7 – 3)^2 + (8 – 4)^2]
= √[4^2 + 4^2]
= √[16 + 16]
= √32
≈ 5.66

So, the distance between points A(3, 4) and B(7, 8) is approximately 5.66 units.

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