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 =
6 = -1 + x2
x2 = 7
10 = 2 + y2
y2 = 10 – 2 = 8
B(x2, y2) is B(7, 8)