HW 1.6

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: c² = a² + b².

Front

How do you calculate the distance between two points in a coordinate plane?

Back

The distance d between two points (x1, y1) and (x2, y2) is calculated using the 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

What is the opposite operation of squaring a number?

Back

The opposite operation of squaring a number is taking the square root.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

5

Front

What is the distance between the points (-5, 5) and (1, -2)?

Back

9.2

Front

Find the midpoint between the numbers -12 and 32.

Back

10

Front

Find the midpoint between the points (2, 7) and (-6, -1).

Back

(-2, 3)

Front

What is the distance formula derived from the Pythagorean theorem?

Back

The distance formula is derived from the Pythagorean theorem and is expressed as d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the square root of 25?

Back

5