Applying the Pythagorean TheoremAdapted from Walch Education

Key ConceptsReviewing Distance on a Number LineTo find the distance between two points, a and b, on a number line, find the absolute value of the difference of a and b. This can be expressed algebraically as |a b| or |b a|.

For example, to find the distance between 4 and 5, take the absolute value of the difference of 4 and 5. |4 5| = |9| = 9 or |5 4| = |5 + 4| = |9| = 9

The distance between the numbers 4 and 5 is 9 units.

Reviewing the Pythagorean Theorem

Right triangles are triangles with one right (90) angle.

The side that is the longest and is always across from the right angle is called the hypotenuse. The two shorter sides are referred to as the legs of the right triangle.

We can use the Pythagorean Theorem to calculate the length of any one of the three sides.

To find the distance between two points on a coordinate system, we can use the Pythagorean Theorem.Finding the Distance Between Two Points Using the Pythagorean TheoremPlot the points on a coordinate system.Draw lines to form a right triangle, using each point as the end of the hypotenuse.Calculate the length of the vertical side, a, of the right triangle by taking the absolute value of the difference of the y-values ( |y2 y1| ).Calculate the length of the horizontal side, b, of the right triangle by taking the absolute value of the difference of the x-values ( |x2 x1| ).Use the Pythagorean Theorem to calculate the length of the hypotenuse, c.

Practice # 1Tyler and Arsha have mapped out locations for a game of manhunt. Tylers position is represented by the point (2, 1). Arshas position is represented by the point (7, 9). Each unit is equivalent to 100 feet. What is the approximate distance between Tyler and Arsha?

Calculate the length of the vertical side, a, of the right triangle.

|y2 y1| = |9 1| = |8| = 8

Calculate the length of the horizontal side, b, of the right triangle.|x2 x1| = |7 2| = |5| = 5

Use the Pythagorean Theorem to calculate the length of the hypotenuse, c.a2 b2 = c2Pythagorean Theorem82 + 52 = c2Substitute values for a and b.64 + 25 = c2Simplify each term.89 = c2Simplify.Take the square root of both sides of the equation.

The distance between Tyler and Arsha is approximately 9.4 units or 940 feet.

Practice # 2Kevin is standing 2 miles due north of the school. James is standing 4 miles due west of the school. What is the distance between Kevin and James?

Thanks for Watching!!!!~ Ms. Dambreville