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: a² + b² = c².

Front

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

Back

The distance between two points can be found using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the formula for finding the midpoint between two points?

Back

The midpoint M between two points (x1, y1) and (x2, y2) is given by the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If one leg of a right triangle is 9 cm and the hypotenuse is 15 cm, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + b² = c². Here, a = 9 cm and c = 15 cm. Solve for b: b = √(c² - a²) = √(15² - 9²) = √(225 - 81) = √144 = 12 cm.

Front

What is the perimeter of a right triangle?

Back

The perimeter of a right triangle is the sum of the lengths of all three sides: P = a + b + c, where a and b are the legs and c is the hypotenuse.

Front

How do you calculate the total distance traveled in a multi-segment journey?

Back

Add the distances of each segment of the journey together to find the total distance traveled.

Front

What is 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 significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Front

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

Back

Use the Pythagorean Theorem: if you know the lengths of two sides, you can find the third side by rearranging the formula a² + b² = c².

Front

What is the midpoint between the points (3, -1) and (7, -5)?

Back

Using the midpoint formula: M = ((3 + 7)/2, (-1 + (-5))/2) = (5, -3).