midpoint and distance formula

Front

What is the midpoint formula?

Back

The midpoint formula is used to find the midpoint (M) of a line segment with endpoints (x1, y1) and (x2, y2). It is given by: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the distance formula?

Back

The distance formula is used to find the distance (d) between two points (x1, y1) and (x2, y2) in a coordinate plane. It is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

Find the distance between the points (1, 2) and (4, 6).

Back

The distance is √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

The midpoint is ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Front

If A = (2, 3) and B = (4, 7), what is the midpoint M of segment AB?

Back

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

Front

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

Back

The distance is √((2 - (-1))² + (2 - (-1))²) = √(3² + 3²) = √(9 + 9) = √18 = 3√2.

Front

Find the midpoint of the segment with endpoints (0, 0) and (10, 10).

Back

The midpoint is ((0 + 10)/2, (0 + 10)/2) = (5, 5).

Front

Point M with coordinates (5, 5) is the midpoint of the line segment AB. If A has coordinates (2, 3), what are the coordinates of B?

Back

B = (2*5 - 2, 2*5 - 3) = (8, 7).

Front

What is the distance between the points (3, 4) and (3, 8)?

Back

The distance is √((3 - 3)² + (8 - 4)²) = √(0 + 4²) = √16 = 4.

Front

Find the distance between the points (-3, -4) and (1, 2).

Back

The distance is √((1 - (-3))² + (2 - (-4))²) = √(4² + 6²) = √(16 + 36) = √52 = 2√13.