Lines and the Coordinate Plane: The Coordinate Plane

The Midpoint Formula

We know that any segment has one and only one midpoint that is equidistant from the endpoints. Given A(x1, y1) and B(x2, y2) are the endpoints of a segment, we can determine the coordinates of its midpoint M. Denoting the coordinates of M by (xm, ym), we will use the following formulas to calculate the midpoint of AB:

xm = x 1 plus x 2 divided by 2 and ym = y 1 y 2 divided by 2

 

You are taking the average of the x-values and the average of the y-values.

Example 1:

Let’s try this example. Given A(4, 11) and B(-8, 15) we will calculate the coordinates of the midpoint M, of AB:

xm = 4 plus negative 8 divided by 2

      = negative 4 divided by 2

      = -2

ym = 11 plus 15 divided by 2

      = 26 divided by 2

      = 13

Thus, M is located at (-2, 13).

Example 2:

Find the midpoint of CD if C (1,-3) and D (-2,-7).

Midpoint for the x coordinate = x 1 plus x 2 divided by 2

    Midpoint of x = 1 plus negative 2 divided by 2

    Midpoint of x = 1 minus 2 divided by 2 equals negative one-half

Midpoint for the y coordinate = y 1 plus y 2 divided by 2

    Midpoint of x = negative 3 plus negative 7 divided by 2

    Midpoint of x = negative 3 minus 7 divided by 2

    Midpoint of x = negative 19 divided by 2 equals negative 5

So the midpoint of CD is sitting at the point the ordered pair, negative on-half, negative 5