Midpoint Practice

Front

What is the definition of a midpoint in geometry?

Back

The midpoint of a line segment is the point that divides the segment into two equal parts. It is calculated as the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Front

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

Back

The midpoint M is given by the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

Find the midpoint of the points (2, 3) and (4, 7).

Back

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

Front

What is the formula to find the endpoint of a segment when given one endpoint and the midpoint?

Back

If A(x1, y1) is one endpoint and M(xm, ym) is the midpoint, the other endpoint B(x2, y2) can be found using: x2 = 2*xm - x1 and y2 = 2*ym - y1.

Front

Given the midpoint (5, -3) and one endpoint (3, -1), find the other endpoint.

Back

Using the formula: x2 = 2*5 - 3 = 7 and y2 = 2*(-3) - (-1) = -5. The other endpoint is (7, -5).

Front

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

Back

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

Front

If point A is at (1, 2) and point B is at (3, 4), what is the midpoint?

Back

The midpoint is ((1 + 3)/2, (2 + 4)/2) = (2, 3).

Front

How do you determine if a point is the midpoint of a segment?

Back

A point is the midpoint if it is equidistant from both endpoints of the segment.

Front

Find the endpoint of the segment with endpoint (5, 1) and midpoint (3, 3).

Back

Using the formula: x2 = 2*3 - 5 = 1 and y2 = 2*3 - 1 = 5. The endpoint is (1, 5).

Front

What is the significance of the midpoint in coordinate geometry?

Back

The midpoint is significant as it helps in determining the center of a line segment, which is useful in various geometric constructions and proofs.