Pythagorean Theorem, Distance, and Midpoint

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 midpoint formula?

Back

The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

Find the endpoint of the segment with endpoint (3, -2) and midpoint (5, 4).

Back

(7, 10)

Front

Find the endpoint of the segment with endpoint (-4, 5) and midpoint (7, -9).

Back

(18, 13)

Front

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

Back

12 cm (using Pythagorean Theorem: 5² + b² = 13²).

Front

Find the length of the missing side if one side is 60 in. and the hypotenuse is 80 in.

Back

80 in.

Front

How do you calculate the length of a side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

What is the distance between the points (2, 3) and (5, 7)?

Back

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

Front

What is the distance between the points (1, 1) and (4, 5)?

Back

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