Distance Formula

Distance Formula The distance between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by the formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ E...

Distance Formula

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

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

Explanation:

The distance $d$ is a non-negative real number representing the shortest distance between the two points.
The coordinates $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
The formula uses the square root function to calculate the distance.
The distance between points with coordinates $(x_1, y_1)$ and $(x_2, y_2)$ can be found by applying the formula.

Examples:

If two points are located at (3, 4) and (7, 10), then the distance between them is:

$d = \sqrt{(7 - 3)^2 + (10 - 4)^2} = \sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52} = 7\sqrt{2}$

If two points are located at (-2, 3) and (4, 7), then the distance between them is:

$d = \sqrt{(4 + 2)^2 + (7 - 3)^2} = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52} = 7\sqrt{2}$