Distance Formula

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

To calculate the distance, use the formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

In the Distance Formula, $$x_1$$ and $$y_1$$ are the coordinates of the first point, and $$x_2$$ and $$y_2$$ are the coordinates of the second point.

Using the Distance Formula: $$d = \sqrt{(5 - 3)^2 + (2 - 0)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$$ .

Using the Distance Formula: $$d = \sqrt{(-1 - (-5))^2 + (-16 - (-8))^2} = \sqrt{(4)^2 + (-8)^2} = \sqrt{16 + 64} = \sqrt{80} = 8.9$$ .

Using the Distance Formula: $$d = \sqrt{(8 - (-3))^2 + (-42 - (-11))^2} = \sqrt{(11)^2 + (-31)^2} = \sqrt{121 + 961} = \sqrt{1082} = 32.9$$ .

Using the Distance Formula: $$d = \sqrt{(2 - 2)^2 + (-6 - (-4))^2} = \sqrt{0 + (-2)^2} = \sqrt{4} = 2$$ .

Using the Distance Formula: $$d = \sqrt{(3 - 8)^2 + (-4 - 8)^2} = \sqrt{(-5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13$$ .

The Distance Formula is significant as it allows us to find the length of a line segment between two points, which is fundamental in geometry and various applications.

The geometric interpretation of the Distance Formula is that it represents the length of the straight line connecting two points in a Cartesian plane.