Midpoint of an interval, i.e. two points A (x_{1}, y_{1}) and B (x_{2}, y_{2}) is obtained by finding the mid value along x and y coordinates separately.

So the midpoint along the x axis = and the midpoint along the y axis = .

Therefore midpoint of the line AB is

## Examples of midpoint of an interval

**Example 1**: Find the midpoint of A (-3, 2) and B (3, 5)

Midpoint of AB =

=

=

**Example 2**: ABCD is a quadrilateral with coordinates A(1, -1), B(3, 5), C(7, 7) and D(5, 1). Find the midpoints of AC and BD to prove ABCD is a parallelogram.

Midpoint of AC =

=

=

Midpoint of BD =

=

=

The midpoints off the diagonals AC and BD are both (4, 3). Hence the diagonals bisect each other. Therefore ABCD is a parallelogram.

**Example 3**: The point M(3, 5) is the midpoint of the interval AB where A is the point (-1, 2). Find the coordinates of B.

Here we’ve been given the midpoint and one of the coordinates, and need to find the other coordinate.

Midpoint of an interval =

3 =

6 = -1 + x_{2}

x_{2} = 7

5 =

10 = 2 + y_{2}

y_{2} = 10 – 2 = 8

B(x_{2}, y_{2}) is B(7, 8)