Question

Pythagorean Theorem:

Alex leaves home, travels 5 miles east, and arrives at the library. He leaves the library and travels 3 miles north to a friend's house. This trip can be plotted on the coordinate plane, where home is the point (0, 0). Alex wants to find out how far his house is from his friend's house and uses the distance formula. Which other formula can he use?

A) 5² - 3²
B) 5² + 3²
C) √5² - 3²
D) √5² + 3²

Hint: The path that Alex traveled is a right triangle.

Explain your answer clearly and thoroughly. Thank you! :D

Answer 1

d

Explanation:

Alex can also use the Pythagorean Theorem (leg2 + leg2 = hypotenuse2), since the path that he traveled formed a right triangle. The legs of the triangle have lengths 5 and 3. The correct answer is

52 + 32

Answer 2

Solutions

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c².

Given

Alex leaves home, travels 5 miles east, and arrives at the library. He leaves the library and travels 3 miles north to a friend's house.

Home would be α
Library would be β
Friends house would be c

Now we have points α β c.

a² (house) + β² ( library) = c² (friends house)

To solve the problem he will have to use this formula. √5² + 3² .
5² (a) + 3² (β).

Correct answer = (D)