Retake 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 can be 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 (x1, y1) and (x2, y2) can be calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

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) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

If the coordinates of point A are (3, 4) and point B are (7, 1), what is the distance between them?

Back

Using the distance formula: d = √((7 - 3)² + (1 - 4)²) = √(4 + 9) = √13 ≈ 3.6.

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 ensure structures are built correctly.

Front

What is 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 are the coordinates of the midpoint between the points (2, 3) and (4, 7)?

Back

The midpoint M can be calculated as: M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Front

How do you determine if a triangle is a right triangle using the lengths of its sides?

Back

To determine if a triangle with sides a, b, and c is a right triangle, check if a² + b² = c², where c is the longest side.

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.

Front

What is the formula for the area of a right triangle?

Back

The area A of a right triangle can be calculated using the formula: A = (1/2) * base * height.