Midpoint and Distance Review

Front

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

Back

The midpoint M is given by M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right).

Front

Given endpoint C (2, -4) and midpoint M (5, -3), how do you find the other endpoint?

Back

Use the midpoint formula: M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right). Rearranging gives x2 = 2M - x1 and y2 = 2M - y1.

Front

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

Back

The distance d is given by d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Front

Find the midpoint between (3, 9) and (3, 3).

Back

The midpoint is (3, 6).

Front

Find the distance between (-12, 1) and (12, -1).

Back

The distance is 24.08.

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts.

Front

How do you find the other endpoint if you know one endpoint and the midpoint?

Back

Use the formula: Other endpoint = 2(Midpoint) - Known endpoint.

Front

What is the distance between (-5, -8) and (-1, -16)?

Back

The distance is 8.9.

Front

If the midpoint of a segment is (0, 0) and one endpoint is (4, 4), what is the other endpoint?

Back

The other endpoint is (-4, -4).

Front

What is the relationship between the coordinates of the midpoint and the endpoints?

Back

The coordinates of the midpoint are the averages of the coordinates of the endpoints.