What is the distance formula between two points (x1, y1) and (x2, y2)?

The distance formula between two points in a Cartesian coordinate system, given as (x1, y1) and (x2, y2), is derived from the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (which corresponds to the distance between the two points) is equal to the sum of the squares of the lengths of the other two sides.

In the context of the distance formula, the change in the x-coordinates (x2 - x1) represents one side of the triangle, and the change in the y-coordinates (y2 - y1) represents the other side. Thus, you would first calculate the differences: (x2 - x1) for the horizontal distance and (y2 - y1) for the vertical distance.

According to the Pythagorean theorem, the distance (d) is given by:

[ d = \sqrt{(x2 - x1)² + (y2 - y1)²} ]

This is exactly what option B states.

The other choices do not correctly represent the distance formula. The first option suggests a summation of absolute differences, which does not give the correct