What is the distance formula in coordinate geometry?

The distance formula in coordinate geometry is derived from the Pythagorean theorem. It is used to calculate the straight-line distance between two points in a Cartesian plane. The formula can be expressed as:

Distance = √((x2 - x1)² + (y2 - y1)²)

In this context, (x1, y1) and (x2, y2) are the coordinates of the two points. The differences (x2 - x1) and (y2 - y1) represent the horizontal and vertical distances between the points, respectively. By squaring these differences, you ensure that both values are treated as positive, which reflects the nature of distance. The square root is then taken to obtain the actual distance, yielding a non-negative result.

This formula directly relates to the construction of a right triangle, where the lengths of the legs correspond to the differences in the x-coordinates and y-coordinates. Applying the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse, leads to the current distance formula.

Understanding this formula enables effective calculation of distances between points, which is foundational for many applications in geometry, physics