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 (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 a right triangle has legs of length 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and computer graphics to calculate distances and create right angles.

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

Find 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 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

If the distance between two points is 10 units and one point is (2, 3), what could be the coordinates of the other point?

Back

Possible coordinates could be (2 + 10, 3) = (12, 3) or (2 - 10, 3) = (-8, 3) or (2, 3 + 10) = (2, 13) or (2, 3 - 10) = (2, -7).

Front

What is the distance between the points (5, 5) and (5, 10)?

Back

Using the distance formula: d = √((5 - 5)² + (10 - 5)²) = √(0 + 25) = √25 = 5 units.