Pythagorean Theorem --> Distance Between Two Points

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points in a Cartesian coordinate system.

Front

If the coordinates of two points are (3, 4) and (7, 1), what is the distance between them?

Back

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

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial in applying the Pythagorean Theorem.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

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 construction, navigation, and computer graphics, to calculate distances and angles.

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 finding the length of a side in a right triangle if the lengths of the other two sides are known?

Back

If the lengths of the two legs (a and b) are known, the length of the hypotenuse (c) can be found using c = √(a² + b²).

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.