Distance Formula and Pythagorean Theorem Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as c² = a² + b².

Front

What is the formula to calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

What does 'c' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse of a right triangle.

Front

What are the coordinates of point A if the distance between points A(2, 3) and B(5, 7) is 5?

Back

Point A is (2, 3) and point B is (5, 7). The distance can be calculated using the distance formula.

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10.

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, as stated by the Pythagorean Theorem.

Front

How do you simplify the expression √(81)?

Back

The simplified form of √(81) is 9.

Front

What is the distance between the points (-3, -4) and (5, 5)?

Back

Using the distance formula: d = √((5 - (-3))² + (5 - (-4))²) = √((5 + 3)² + (5 + 4)²) = √(8² + 9²) = √(64 + 81) = √145, which is approximately 12.04.

Front

What is the formula for finding the length of a side in a right triangle if the hypotenuse and one leg are known?

Back

If the hypotenuse (c) and one leg (a) are known, the length of the other leg (b) can be found using: b = √(c² - a²).