How do you find the distance between two points (x1, y1) and (x2, y2)?

To find the distance between two points ((x_1, y_1)) and ((x_2, y_2)) in a Cartesian coordinate system, you can use the distance formula, which is derived from the Pythagorean theorem. The correct formula is as follows:

[

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

]

This formula calculates the straight-line distance between the two points. Each component ( (x_2 - x_1) ) and ( (y_2 - y_1) ) represents the horizontal and vertical distances between the two points respectively. Squaring these components ensures that the distance is non-negative, as distance cannot be negative, and then summing them follows the Pythagorean theorem where the distance forms the hypotenuse of a right triangle whose other sides are the differences in the x and y coordinates.

The correct answer captures this relationship through the calculation, yielding the same result regardless of the order of the coordinates due to the properties of squaring and addition.