How do I find the distance between two points using the distance formula?

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by √[(x₂ − x₁)² + (y₂ − y₁)²]. The idea is that the horizontal gap is (x₂ − x₁) and the vertical gap is (y₂ − y₁), and the straight-line distance is the hypotenuse, so Pythagoras gives the formula. For example, the distance between A(1, 2) and B(4, 6) is √[(4 − 1)² + (6 − 2)²] = √[9 + 16] = √25 = 5. A common mistake is forgetting to square, or mixing up x and y. Subtract the matching coordinates, square each difference (so signs do not matter), add them, and take the square root at the end.