Midpoint Formula

The midpoint is the point exactly half-way between two given points in a coordinate system. You can describe it as the balancing point, connecting both of the given points, on that line segment.

One finds the average of the x-coordinates and the average of the y-coordinates between the two points, thereby obtaining a third point equidistant to the two endpoints.

Definition: Midpoint formula gives the midpoint of two points on a coordinate plane. This is an exact middle point.

Formula

If you have two points,   , the midpoint M can be calculated using the formula:

Solved Problems

Problem 1: Find the midpoint of a line whose endpoints are (4, 5) and (6, 7).

Solution:

 (x, y) = [(4 + 6)/2, (5 + 7)/2]

 = (5, 6)

Problem 2: If (1, 0) is the midpoint of the line joining the points A(-6, -5) and B, then find the coordinates of B.

Solution:

Now equating the x and y coordinates,
(a – 6)/2 = 1, (b – 5)/2 = 0
a – 6 = 2, b – 5 = 0
a = 8, b = 5
Therefore, the coordinates of B = (8, 5).

Problem 3: Find the coordinates of the center of the circle whose endpoints of a diameter are (0, 2), (3, 4).
Solution:

= [(0 + 3)/2, (2 + 4)/2]

= (3/2, 6/2)

= (1.5, 3)

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