5.1 Distance and Midpoint

Front

What is the midpoint formula?

Back

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

Front

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

Back

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

Front

If M is the midpoint of line segment AB, and A has coordinates (x1, y1), how do you find the coordinates of B?

Back

Use the formula B = (2Mx - x1, 2My - y1), where M is the midpoint.

Front

What is the distance between the points (1, 3) and (5, 6)?

Back

The distance is 5.

Front

Given the midpoint (3, 4) and one endpoint (-1, 6), what is the other endpoint?

Back

The other endpoint is (7, 2).

Front

What is the distance between the points (-12, 1) and (12, -1)?

Back

The distance is 24.08.

Front

Define 'midpoint' in the context of geometry.

Back

The midpoint is the point that divides a line segment into two equal parts.

Front

What is the significance of the distance formula in geometry?

Back

The distance formula allows us to calculate the length of a line segment between two points in a coordinate plane.

Front

How can you verify if a point is the midpoint of a line segment?

Back

Check if the coordinates of the point satisfy the midpoint formula for the endpoints of the segment.

Front

What are the coordinates of the midpoint of the line segment with endpoints (2, 3) and (4, 7)?

Back

The midpoint is (3, 5).