The Distance Formula

Two friends enter a park from different entrances and stop at different corners of a field.

From their respective positions, they want to determine the exact distance between them.

The distance formula is applied to calculate the distance between the two positions, marked as points A and B, using their coordinates.

It finds the shortest path between them—like cutting diagonally across a field instead of walking around the edges.

This calculation is based on the Pythagorean Theorem, where the horizontal and vertical distances meet at Point C, forming a right triangle.

The theorem states that the square of the hypotenuse, or the diagonal side, equals the sum of the squares of the other two sides.

On a coordinate grid, these sides represent the differences in the x- and y-values between points A and B.

By squaring the horizontal and vertical differences, adding them together, and taking the square root, the length of the hypotenuse is determined.

This relationship gives the straight-line distance between the two friends.

Such calculations are also used in mapping routes and planning wireless network coverage.