Master The Distance Formula: A Comprehensive Guide To Calculating Distances In A 2D/3D Plane Using Pythagorean Theorem

Distance Formula


The distance formula is a mathematical equation used to calculate the distance between two points in a two or three-dimensional plane. The distance formula is based on the Pythagorean theorem which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

The distance formula can be represented as follows:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Where d stands for distance, (x1, y1) and (x2, y2) represent the coordinates of the two points on the plane, x and y are the horizontal and vertical dimensions respectively.

To use the distance formula, we need to know the values of (x1, y1) and (x2, y2) of the two points. We then simply plug these values into the equation and solve for the distance.

For example, to find the distance between points A (2,3) and B (5,7), we first label each point’s coordinates as x1=2, y1=3 and x2=5, y2=7, respectively. Then, we substitute these values into 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.

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