Pythagorean Theorem Applications

This video tutorial explains how to find the distance between two points on a graph using the Pythagorean theorem. It begins with an introduction to the concept, followed by several examples. The first example involves a given right triangle, while the second requires counting units on a graph. The third example applies the theorem to a real-world scenario, and the fourth provides additional practice. Throughout, the video emphasizes the importance of understanding the relationship between the legs and hypotenuse of a right triangle.

What is the first step in finding the distance between two points on a graph using the Pythagorean theorem?

• Form a right triangle by extending lines

• Draw a circle around the points

• Calculate the midpoint of the line

• Connect the points to form a line

In the first example, what is the value of 'a' used in the Pythagorean theorem?

• 8

• 6

• 2

• 4

How do you determine the length of the hypotenuse in the first example?

• By multiplying the lengths of the legs

• By using the Pythagorean theorem and taking the square root

• By subtracting the lengths of the legs

• By adding the lengths of the legs

What is the main difference between the first and second examples?

• The second example is not on a graph

• The second example uses a different formula

• The second example requires counting units

• The second example has a larger hypotenuse

In the second example, what is the length of the hypotenuse after calculation?

• 7.2

• 6.4

• 5.0

• 8.1

What is the distance between Francesca's house and the beach house?

• 200 meters

• 306 meters

• 144 meters

• 270 meters

How is the base of the triangle determined in Francesca's example?

• By measuring directly

• By subtracting the x-values

• By using a ruler

• By adding the y-values

What is the approximate distance from Francesca's house to Camp Sunshine?

• 214.7 meters

• 190 meters

• 100 meters

• 306 meters

Why is a calculator recommended for the Camp Sunshine example?

• To convert units

• To draw the triangle accurately

• To ensure precise calculations

• To measure the distance directly

What is the formula used to find the distance between two points?

• a + b = c

• a^2 * b^2 = c^2

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2