Distance Formula

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

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): $$a^2 + b^2 = c^2$$ .

The triangle must be a right triangle.

The longest side of a right triangle is called the hypotenuse.

Using the Pythagorean Theorem: $$c = \sqrt{14^2 + 27^2} = 31$$ .

A 'leg' refers to either of the two shorter sides of a right triangle that form the right angle.

Use the Distance Formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The formula is $$c = \sqrt{a^2 + b^2}$$ .

Using the Pythagorean Theorem: $$c = \sqrt{3^2 + 4^2} = 5$$ .