Distance (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 is expressed as: c² = a² + b².

Front

How do you calculate the distance between two points in a coordinate plane?

Back

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

Front

What is the distance formula derived from?

Back

The distance formula is derived from the Pythagorean Theorem, where the distance between two points forms the hypotenuse of a right triangle.

Front

What is the length of the diagonal of a rectangle with vertices at (x1, y1), (x2, y1), (x2, y2), and (x1, y2)?

Back

The length of the diagonal can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a rectangle has a width of 6 units and a height of 8 units, what is the length of its diagonal?

Back

Using the Pythagorean Theorem, the diagonal d = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

Front

What is the significance of the coordinates (-6, -4) and (1, 3) in calculating distance?

Back

These coordinates represent two points in a Cartesian plane, and their distance can be calculated using the distance formula.

Front

How do you find the distance between points (2, 4) and (2, -4)?

Back

Using the distance formula: d = √((2 - 2)² + (-4 - 4)²) = √(0 + 64) = √64 = 8 units.

Front

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

Back

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

Front

What is the relationship between the lengths of the sides of a right triangle and the Pythagorean Theorem?

Back

The lengths of the two shorter sides (legs) of a right triangle can be used to find the length of the hypotenuse using the Pythagorean Theorem: c² = a² + b².

Front

How can the Pythagorean Theorem be applied in real-world scenarios?

Back

The Pythagorean Theorem can be used in various real-world applications, such as determining distances, construction, navigation, and in physics.