Distance Formula, Pythagorean Theorem, Converse

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What does the Pythagorean Theorem state?

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: a² + b² = c².

Front

What is the Converse of the Pythagorean Theorem?

Back

The Converse of the Pythagorean Theorem states that if in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

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

Back

Use the Distance Formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (3, 4) and (0, 0)?

Back

Using the Distance Formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

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

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Front

What is the length of the missing side if one side is 5 cm and the hypotenuse is 13 cm?

Back

Using the Pythagorean Theorem: a = √(c² - b²) = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.

Front

Find the distance between the points (-5, -8) and (-1, -16).

Back

Using the Distance Formula: d = √((-1 - (-5))² + (-16 - (-8))²) = √((4)² + (-8)²) = √(16 + 64) = √80 ≈ 8.9.

Front

What is the coordinate of point Z if it is at (4, -6)?

Back

The coordinate of point Z is (4, -6).

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

Check if a² + b² = c² holds true for the lengths of the sides.