# Algebra 1 pythagorean theorem and distance formula worksheet

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## Distance Formula

Worksheet by Kuta Software LLC. Algebra 1 Pythagorean Theorem & Distance Formula. Find each missing length to the nearest tenth. 1). 6. 2). 7. 9. 3). 6.

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Check out the distance formula calculator near the end of this page that can calculate the distance between two points. Use it to check your answers. In the coordinate plane, we can use the distance formula to find the distance between any two points. The distance formula can be derive from the Pythagorean Theorem. The distance between the two points x 1 ,y 1 and x 2 ,y 2 is given by the distance formula. Example: To find the distance between the points P 2, 3 and Q 1, 1. In general, the distance between two points P x 1 , y 1 and Q x 2 , y 2 is given by the distance formula :.

Here is a graphic preview for all of the Pythagorean Theorem Worksheets. You can select different variables to customize these Pythagorean Theorem Worksheets for your needs. The Pythagorean Theorem Worksheets are randomly created and will never repeat so you have an endless supply of quality Pythagorean Theorem Worksheets to use in the classroom or at home. Our Pythagorean Theorem Worksheets are free to download, easy to use, and very flexible. Pythagorean Theorem Practice Problems Worksheets This Pythagorean Theorem Problems Worksheet will produce problems for practicing solving the lengths of right triangles. You may choose the type of numbers and the sides of the triangle. This worksheet is a great resources for the 6th Grade, 7th Grade, and 8th Grade.

The distance formula is used to find the distance between two points in the coordinate plane. We'll explain this using an example below. We want to calculate the distance between the two points -2, 1 and 4, 3. We could see the line drawn between these two points is the hypotenuse of a right triangle. The legs of this triangle would be parallel to the axes which mean that we can measure the length of the legs easily.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Basic geometry Pythagorean theorem Pythagorean theorem and distance between points. Finding distance with Pythagorean theorem. Practice: Distance between two points. Distance formula review.

## The distance and midpoint formulas

The very essence of the Distance formula is to calculate the length of the hypotenuse of the right triangle which is represented by the letter c. Below is an illustration showing that the Distance Formula is based on the Pythagorean Theorem where the distance d is the hypotenuse of a right triangle. Plugging in the values of x and y , we get:. Sometimes you may wonder if switching the points in calculating the distance can affect the final outcome. Well, if you think about it, the formula is squaring the difference of the corresponding x and y values.

Derived from the Pythagorean Theorem , the distance formula is used to find the distance between two points in the plane. We use the absolute value symbol to indicate that the length is a positive number because the absolute value of any number is positive. To find the length c , take the square root of both sides of the Pythagorean Theorem. We do not have to use the absolute value symbols in this definition because any number squared is positive. Let us first look at the graph of the two points. On the way, she made a few stops to do errands.

The distance formula is derived from the Pythagorean theorem. Round your answer to the nearest tenth. Note, it does not matter which 'way' you draw the right triangle. It can be either up above or down below. Solve for the Hypotenuse. Notice the line colored green that shows the same exact mathematical equation both up above, using the pythagorean theorem, and down below using the formula.

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