Calculating Distances in a Coordinate Plane | Understanding the Distance Formula and Its Applications

distance formula

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

The distance formula is used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and applies to any two-dimensional or three-dimensional space.

In two dimensions, the distance formula is given by:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Here, (x1, y1) represents the coordinates of the first point, and (x2, y2) represents the coordinates of the second point. The formula essentially finds the horizontal distance (Δx) and vertical distance (Δy) between the two points, squares them, adds them together, and then takes the square root of the sum to obtain the distance (d).

For example, let’s say we have two points A(2, 3) and B(5, 7). We can use the distance formula to find the distance between them:

d = √((5 – 2)^2 + (7 – 3)^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5

Therefore, the distance between points A and B is 5 units.

The distance formula can also be extended to three dimensions, where the coordinates of points A and B would consist of (x1, y1, z1) and (x2, y2, z2) respectively.

It is important to note that the distance formula can be used in various applications, such as calculating the length of a line segment, the distance traveled between two locations, or determining the shortest distance between two points.

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