EGR - Distance Formula Lesson

Distance Formula

In this lesson, we will learn how to determine the distance between two points on the Coordinate Plane and how to apply the distance formula.

The Pythagorean Theorem can determine the length between two points on the coordinate plane. To identify the leg lengths, find the distance between the two and the two of the given points. Use these lengths to apply the Pythagorean Theorem to determine the hypotenuse.

Image of two graphs illustrating the distance between points. They are applying the Pythagorean theorem to do this.

There is a formula that allows us to find the distance between two points on a coordinate plane.

Distance Formula-Change in X and Change in Y)

The changes in the x and y values represent the leg lengths a and b for the right triangle, and the distance represents the hypotenuse. Using this formula, you do not have to have the coordinate plane in order to find the distance.

Look at the following problem:

$LaTeX: D=\sqrt{(-6-2)^2+(-6-6)^2}$ $D=\sqrt{(-6-2)^2+(-6-6)^2}$

$LaTeX: D=\sqrt{-8^2+\sqrt{-12^2}}$ $D=\sqrt{-8^2+\sqrt{-12^2}}$

$LaTeX: D=\sqrt{64+144}$ $D=\sqrt{64+144}$

$LaTeX: D=\sqrt{208}$ $D=\sqrt{208}$

$LaTeX: D\approx14.4$ $D\approx14.4$

Now that you have learned the two methods for finding the distance between two points on a coordinate plane, you can apply these to solving problems involving graphs.

Try it!

1. Which expression represents the distance between the points graphed below?

2. The vertices of a triangle are A(1,2), B(3, 4) and C(4, 1). What is the length of the shortest side of the triangle? $LaTeX: \sqrt{8}\approx2.8$ $\sqrt{8}\approx2.8$

3. Find the length of the hypotenuse of the triangle.

Solutions:

1. $LaTeX: \sqrt{578}\approx24$ $\sqrt{578}\approx24$

2. $LaTeX: \sqrt{8}\approx2.8$ $\sqrt{8}\approx2.8$

3. appox. 11.18 units

Practice

If you would like to practice these types of problems and check your work before you complete your graded homework assignment, click here. Links to an external site. Make sure you check your answers and look at the course resources or ask your teacher if there are any problems you do not understand. Links to an external site.

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