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 based on the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a two-dimensional coordinate plane, if we have two points with coordinates (x1, y1) and (x2, y2), we can calculate the distance between them using the distance formula:
d = √((x2 – x1)^2 + (y2 – y1)^2)
Here, “d” represents the distance between the two points. This formula can also be extended to three dimensions by considering the z-coordinate as well.
To use the formula, we simply substitute the given coordinates into the formula and calculate the square roots if necessary.
For example, let’s say we have two points A(2, 3) and B(5, 7). To find the distance between them, we can use the distance formula:
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 is a useful tool in mathematics and is used in various fields such as geometry, physics, and engineering to calculate distances between objects or points in space.
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