midpoint and distance formula

Front

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

Back

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

Front

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

Back

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

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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): c² = a² + b².

Front

What is the opposite operation of squaring a number?

Back

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

Front

What is the midpoint of the segment with endpoints (2, 4) and (8, 10)?

Back

The midpoint is (5, 7).

Front

If the coordinates of two points are (3, 4) and (7, 1), what is the distance between them?

Back

The distance is √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Front

What is the distance between the points (0, 0) and (x, y)?

Back

The distance is √(x² + y²).

Front

How do you find the coordinates of the midpoint of a vertical line segment?

Back

For a vertical line segment with endpoints (x, y1) and (x, y2), the midpoint is (x, (y1 + y2)/2).

Front

How do you find the coordinates of the midpoint of a horizontal line segment?

Back

For a horizontal line segment with endpoints (x1, y) and (x2, y), the midpoint is ((x1 + x2)/2, y).