How do you calculate the distance between two points in a coordinate plane?

The distance between two points in a coordinate plane can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Suppose we have two points in the coordinate plane, represented by the coordinates (x1, y1) and (x2, y2). The distance between these two points can be calculated using the following formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Here, sqrt denotes the square root function, and (^) denotes exponentiation.

For example, suppose we want to find the distance between the points (2, 3) and (5, 7). Using the formula above, we can calculate the distance as follows:

distance = sqrt((5 - 2)^2 + (7 - 3)^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5

Therefore, the distance between the points (2, 3) and (5, 7) is 5 units.