Distance and 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: a² + b² = c².

Front

How do you find 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 square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x.

Front

If one leg of a right triangle is 3 cm and the other leg is 4 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Front

What is the perimeter of a right triangle with legs of 3 cm and 4 cm?

Back

The perimeter P is the sum of all sides: P = 3 cm + 4 cm + 5 cm = 12 cm.

Front

What is the distance traveled if a person goes 3 miles north and then 4 miles east?

Back

Using the Pythagorean Theorem: d = √(3² + 4²) = √(9 + 16) = √25 = 5 miles.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

In a right triangle, if one angle is 90 degrees, what are the other two angles?

Back

The other two angles must add up to 90 degrees, as the sum of angles in a triangle is always 180 degrees.

Front

If the coordinates of point A are (1, 2) and point B are (4, 6), what is the distance between them?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the formula for the perimeter of a triangle?

Back

The perimeter P of a triangle is the sum of the lengths of its sides: P = a + b + c.