Algebra 1 - Distance, Midpoint & Pythagorean Theorem Flashcard

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 find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. If you know the lengths of two sides, you can rearrange the formula to solve for the missing side.

Front

What is the formula for finding the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint formula is: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If a right triangle has one leg measuring 24 cm and the other leg measuring 10 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 24² + 10²; c² = 576 + 100; c² = 676; c = √676 = 26 cm.

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.

Front

Find the midpoint of the segment with endpoints (2, 3) and (4, 7).

Back

Midpoint M = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Front

What is the length of the hypotenuse if one leg is 5 cm and the other leg is 12 cm?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = √169 = 13 cm.

Front

How do you find the distance between two points on a coordinate plane?

Back

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

Front

What is the midpoint of the points (1, 2) and (3, 4)?

Back

Midpoint M = ((1 + 3)/2, (2 + 4)/2) = (2, 3).