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 can be expressed as: c² = a² + b².

Front

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

What is the length of a line segment represented by two endpoints (x1, y1) and (x2, y2)?

Back

The length of a line segment is the distance between its two endpoints, calculated using the distance formula.

Front

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

Back

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

Front

What is the significance of the distance formula in geometry?

Back

The distance formula is used to determine the length of a line segment between two points in a coordinate plane, which is fundamental in geometry and various applications.

Front

How do you find the length of a line segment on a coordinate plane?

Back

To find the length of a line segment on a coordinate plane, use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the approximate distance between the points (-10, 3) and (-4, -8)?

Back

Using the distance formula: d = √((-4 - (-10))² + (-8 - 3)²) = √(6² + (-11)²) = √(36 + 121) = √157 ≈ 12.5 units.

Front

What does it mean for a triangle to be a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

Front

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

Back

In a right triangle, the lengths of the sides are related by the Pythagorean Theorem, which allows for the calculation of one side if the lengths of the other two sides are known.