Distance Formula

The Distance Formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: $$d = \text{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$$ .

Using the Distance Formula: $$d = \text{sqrt}((2 - (-2))^2 + (0 - 4)^2) = \text{sqrt}(16 + 16) = \text{sqrt}(32) = 4\text{sqrt}(2)$$ .

Using the Distance Formula: $$d = \text{sqrt}((4 - 1)^2 + (6 - 2)^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

The distance is 0, as there is no separation between the points.

The distance between them is 0, indicating they occupy the same position in the coordinate plane.

The Distance Formula works the same way regardless of whether the coordinates are positive or negative. Just substitute the values into the formula.

Using the Distance Formula: $$d = \text{sqrt}((-1 - 3)^2 + (4 - (-2))^2) = \text{sqrt}((-4)^2 + (6)^2) = \text{sqrt}(16 + 36) = \text{sqrt}(52) = 2\text{sqrt}(13)$$ .

The Distance Formula is essential for calculating lengths of line segments, determining if points are equidistant from a point, and solving problems involving triangles and other shapes.

The result represents the straight-line distance between two points in a two-dimensional space.

Using the Distance Formula: $$d = \text{sqrt}((5 - 0)^2 + (5 - 0)^2) = \text{sqrt}(25 + 25) = \text{sqrt}(50) = 5\text{sqrt}(2)$$ .