Calculating Distances in Math: The Essential Guide to Using the Distance Formula for Precise Measurements

distance formula

if you add or subtract both sides of the inequality

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 and is applicable in two- or three-dimensional space.

In a two-dimensional coordinate plane, 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 computes the horizontal and vertical distances between the two points and uses the Pythagorean theorem to find the hypotenuse, which is the distance between them.

In a three-dimensional coordinate space, the distance formula is slightly modified:

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

Similarly, (x1, y1, z1) represents the coordinates of the first point, and (x2, y2, z2) represents the coordinates of the second point.

To use the distance formula, you need to know the coordinates of the two points in question and simply substitute them into the formula. The result will be the distance between the two points, which can be expressed as a positive number.

For example, if you want to find the distance between point A(2, 3) and point B(5, 7) in a two-dimensional plane, you would substitute the values into the formula:

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

The distance between point A and point B is 5 units.

The distance formula is a fundamental tool in mathematics, physics, and other scientific disciplines. It allows us to measure the distance between points in a precise and systematic manner, providing valuable information for various applications and problem-solving situations.

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