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). Formula: 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 is calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the formula for finding the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

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

Front

If a triangle has sides of lengths 27, 36, and 45, how can you determine if it is a right triangle?

Back

Use the Pythagorean Theorem. Check if 27² + 36² = 45². If true, it is a right triangle.

Front

What is the length of the side CD if the distance is given as 9 units?

Back

The length of side CD is 9 units.

Front

What is the distance traveled by Casey if she goes west to the bank and then north to the mall before returning home?

Back

Casey travels a total of 40 miles.

Front

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

Back

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts.

Front

How can you verify if a triangle is a right triangle using side lengths?

Back

Check if the square of the longest side equals the sum of the squares of the other two sides.