Distance Formula and Pythagorean Theorem Review

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What does the Pythagorean Theorem state?

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: a² + b² = c².

Front

How do you find the distance between the points (x1, y1) and (x2, y2)?

Back

To find the distance, use the Distance Formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

The distance is 5, calculated using the Distance Formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

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

Back

The distance is 12, calculated using the Distance Formula: d = √((5 - (-3))² + (5 - (-4))²) = √(64 + 81) = √145.

Front

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

Back

The distance is √145, calculated using the Distance Formula: d = √((4 - (-5))² + (-5 - 3)²) = √(81 + 64) = √145.

Front

What is the length of the hypotenuse if the other two sides are 30 and 40?

Back

The length of the hypotenuse is 50, calculated using the Pythagorean Theorem: c = √(30² + 40²) = √(900 + 1600) = √2500 = 50.

Front

If one side of a right triangle is 60 and the hypotenuse is 80, what is the length of the other side?

Back

The length of the other side is 70, calculated using the Pythagorean Theorem: b = √(80² - 60²) = √(6400 - 3600) = √2800 = 70.

Front

What is the distance between the points (1, 2) and (1, 5)?

Back

The distance is 3, calculated using the Distance Formula: d = √((1 - 1)² + (5 - 2)²) = √(0 + 9) = √9 = 3.

Front

What is the distance between the points (2, 3) and (2, 3)?

Back

The distance is 0, since both points are the same.