Midpoint and distance formula

Front

What is the distance formula?

Back

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

Front

How do you find the midpoint between two points?

Back

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

Front

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

Back

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

Front

What is the significance of the distance formula in geometry?

Back

The distance formula helps in determining the length of line segments, which is essential for solving problems related to geometry, such as finding the perimeter of shapes.

Front

Calculate the distance between the points (0, 0) and (3, 4).

Back

d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the midpoint of the points (2, 3) and (4, 7)?

Back

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

Front

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

Back

d = √((1 - (-1))² + (1 - (-1))²) = √(2² + 2²) = √(4 + 4) = √8 = 2√2.

Front

What does the distance formula represent in real-world applications?

Back

The distance formula can be used in various real-world applications, such as calculating the distance between two locations on a map.

Front

Find the midpoint between the points (5, 5) and (7, 9).

Back

M = ((5 + 7)/2, (5 + 9)/2) = (6, 7).

Front

Calculate the distance between the points (3, 4) and (3, 10).

Back

d = √((3 - 3)² + (10 - 4)²) = √(0 + 6²) = √36 = 6.