The Distance Formula: Calculate the Distance Between Two Points in a Coordinate Plane Using the Pythagorean Theorem

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 plane, 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)

Where:
– d represents the distance between the two points.
– √ represents the square root.
– (x1, y1) and (x2, y2) are the coordinates of the two points.

Now, let’s take an example to understand the distance formula better.

Suppose we have two points A(2, 3) and B(4, 7). We want to find the distance between these two points.

Using the distance formula:

d = √((4 – 2)^2 + (7 – 3)^2)
= √(2^2 + 4^2)
= √(4 + 16)
= √20
≈ 4.47 (rounded to two decimal places)

Therefore, the distance between points A(2, 3) and B(4, 7) is approximately 4.47 units.

It’s worth noting that the distance formula can also be extended to three-dimensional space by adding an extra term for the z-coordinate. The formula would then become:

d = √((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

I hope this explanation helps you understand and apply the distance formula effectively in your studies.

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