Pythagorean Theorem and Distance Formula

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). Formula: a² + b² = c².

Front

What is the Distance Formula?

Back

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

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

What is the length of the missing side if one side is 6 and the hypotenuse is 10?

Back

Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8.

Front

Calculate the distance between the points (2, 3) and (5, 7).

Back

Using the Distance Formula: d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the distance between the points (1, 1) and (4, 5)?

Back

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

Front

If Becky walks 6 blocks North and 8 blocks West, how far is she from the starting point?

Back

Using the Pythagorean Theorem: d = √(6² + 8²) = √(36 + 64) = √100 = 10 blocks.

Front

What is the length of the hypotenuse if the legs are 5 and 12?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.

Front

Find the distance between the points (3, 4) and (3, 8).

Back

Using the Distance Formula: d = √((3 - 3)² + (8 - 4)²) = √(0 + 16) = √16 = 4.

Front

What is the distance between the points (0, 0) and (0, 5)?

Back

Using the Distance Formula: d = √((0 - 0)² + (5 - 0)²) = √(0 + 25) = √25 = 5.