Distance Formula

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

Using the Distance Formula: $$d = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$ .

Point A is represented as (x_1, y_1) in the Distance Formula.

Point B is represented as (x_2, y_2) in the Distance Formula.

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

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

Using the Distance Formula: $$d = \sqrt{(3 - (-2))^2 + (4 - (-3))^2} = \sqrt{25 + 49} = \sqrt{74}$$ .

The distance is given by: $$d = \sqrt{x^2 + y^2}$$ .

The distance is the length of the straight line connecting the two points in a coordinate plane.

Using the Distance Formula: $$d = \sqrt{(5 - 5)^2 + (10 - 5)^2} = \sqrt{0 + 25} = 5$$ .