8.7D Distance between two points - Pythagorean Theorem

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 can be expressed as: c² = a² + b².

Front

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

Back

The distance d between two points can be calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (3, 4) and (7, 1)?

Back

Using the distance formula: d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5 units.

Front

If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between them?

Back

Using the distance formula: d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5 units.

Front

What is the hypotenuse of a right triangle with legs of length 6 and 8?

Back

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

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) = √(9 + 16) = √25 = 5 units.

Front

What is the formula for calculating the distance between two points in a coordinate plane?

Back

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

Front

If point C is at (0, 0) and point D is at (3, 4), what is the distance between them?

Back

Using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5 units.

Front

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

Back

Using the distance formula: d = √((2 - 2)² + (1 - 5)²) = √(0 + 16) = √16 = 4 units.

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) = √(9 + 16) = √25 = 5 units.