Distance Formula

The Distance Formula is given by $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ , which calculates the distance between two points (x1, y1) and (x2, y2) in a Cartesian plane.

In the context of coordinates, 'D' can represent a point located at specific coordinates, such as (7, -6) in the given example.

Using the Distance Formula: $$d = \sqrt{(12 - 0)^2 + (1 - 10)^2} = \sqrt{144 + 81} = \sqrt{225} = 15$$ .

The first step is to identify the coordinates of the two points you are measuring the distance between.

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

The square root in the Distance Formula ensures that the distance is a non-negative value, as distance cannot be negative.

The simplified form of $$\frac{9}{3}$$ is 3.

Coordinates refer to a set of values that determine the position of a point in a space, typically represented as (x, y) in a 2D plane.

You apply the Distance Formula in the same way, ensuring to square the differences of the coordinates, which will eliminate any negative signs.

Using the Distance Formula: $$d = \sqrt{(3 - 3)^2 + (0 - 4)^2} = \sqrt{0 + 16} = 4$$ .