Prove: In the plane rectangular coordinate system xoy
Suppose point A (x 1, y 1) and point B (x2, y2).
The midpoint of the line segment AB is the point M(x, y).
Because |AM|=|MB|, and vector AM and vector MB are in the same direction.
So vector AM= vector MB, that is, (x-x 1, y-y 1)=(x2-x, y2-y).
So x-x 1 = x2-x 1, y-y 1 = y2-y2.
We can get 2x=x 1+x2 from ①, so x=(x 1+x2)/2.
2y=y 1+y2 can be obtained from ②, so y=(y 1+y2)/2.
To sum up, the coordinates of point M are ((x 1+x2)/2, (y 1+y2)/2).
Extended data:
Points for attention of midpoint coordinates:
The inclination and slope of the straight line reflect the inclination of the straight line relative to the positive direction of the X axis. For the inclination angle, we should pay attention to three points: the upward direction of the straight line, the positive direction of the X axis, and the minimum positive angle of 0 ≤ α < 180.
Several forms of linear equations are the most important divergence points in this chapter. From the slope formula of a straight line passing through two points, the point-oblique type of a straight line can be derived, which is a special case of point-oblique type, which is derived from two-point type and general type respectively, and the intercept type is a special case of two-point type. Any straight line on the plane corresponds to the binary linear equation of coordinates x and y, and any binary linear equation about x and y is a straight line.