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Why is this concept useful?: The Distance Formula is used to solve problems involving finding the distance between two points. Using this method provides a quicker way than using the Pythagorean Theorem as the Distance Formula is derived from it.
Where does this concept fit into the curriculum?: Grade 8, High School Algebra

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What is the Distance Formula?

The Distance Formula applies the Pythagorean Theorem to find the distance between any two points.

How to Use the Distance Formula:

The distance between two points

(x_1,y_1)

and

(x_2,y_2)

is found using the following formula:

distance = \sqrt{(x_2 - x_1)^2-(y_2-y_1)^2}

This formula is derived from the Pythagorean Theorem:

a^2 + b^2 = c^2

, where the c is the longest side of a right triangle and a and b make up the legs of the right triangle. The distance formula calculates the longest side of the right triangle or the hypotenuse which is represented by c.

Sample Math Problems

Question: What is the distance between the following points?

(2,-3) and (9,-10)

Answer: Use the distance formula to plug in the values where (2,-3) is

(x_1,y_1)

and (9,-10) is

(x_2,y_2)

:

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distance = \sqrt{(x_2 - x_1)^2-(y_2-y_1)^2}

= \sqrt{(9-2)^2-(-10-(-3))^2}

= \sqrt{(7)^2-(-7)^2} = \sqrt{49+49} = \sqrt{98}

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Geometry Worksheets

Distance Formula

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Sample Math Problems

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