Distance Formula

The Distance Formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

In the Distance Formula d = √((x2 - x1)² + (y2 - y1)²), (x1, y1) and (x2, y2) are the coordinates of the two points, and d represents the distance between them.

d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

d = √((2 - (-1))² + (2 - (-1))²) = √(3² + 3²) = √(9 + 9) = √18 = 3√2.

d = √((1 - 1)² + (5 - 2)²) = √(0 + 3²) = √9 = 3.

The Distance Formula is derived from the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (distance) is equal to the sum of the squares of the other two sides.

d = √((4 - 4)² + (4 - 4)²) = √(0 + 0) = √0 = 0.

d = √((6 - 3)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

d = √((3 - 8)² + (-4 - 8)²) = √((-5)² + (-12)²) = √(25 + 144) = √169 = 13.