Midpoint and Distance Review

Front

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

Back

The distance d is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the midpoint of a line segment between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the distance between the points (0,0) and (3,4)?

Back

The distance is 5, calculated using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

What is the distance between the points (-11,4) and (4,4)?

Back

The distance is 15, calculated as: d = √((4 - (-11))² + (4 - 4)²) = √(15² + 0) = 15.

Front

What is the square root of 96 simplified?

Back

The square root of 96 simplifies to 4√6.

Front

If point A is at (-2, 9) and point B is at (6, -3), what is the midpoint of segment AB?

Back

The midpoint is (2, 3), calculated as: M = ((-2 + 6)/2, (9 + (-3))/2) = (2, 3).

Front

What is the distance between two points J and K if the distance is given as 8.2?

Back

The distance between points J and K is simply 8.2.

Front

What does the distance formula represent in a coordinate plane?

Back

The distance formula calculates the straight-line distance between two points in a Cartesian coordinate system.

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts and is often used in various geometric constructions.

Front

How can you determine if two points are the same using the distance formula?

Back

If the distance calculated between two points is 0, then the points are the same.