Midpoint of a Line Segment

Midpoint of a Line Segment

How to solve the midpoint of a line segment problems (on a number line, on a coordinate plane): formula, examples, and their solutions.

Example 1

Find the coordinate of the midpoint of line segment AB: A(-1), B(5).

The coordinate of the midpoint is
the mean of the endpoints' coordinate.

So M = (-1 + 5)/2.

Example 2

Find the coordinate of the midpoint of line segment AB: A(-3, 1), B(5, 4).

The coordinates of the midpoint are
the means of the endpoints' coordinates.

So M[(-3 + 5)/2, (1 + 4)/2] = [1, 3/2].

Example 3

Find the coordinate of Q(a, b): P(-4, 5), M(0, 2).

The coordinates of the midpoint are
the means of the endpoints' coordinates.

So M[(-4 + a)/2, (5 + b)/2] = M[0, 2].

Then (-4 + a)/2 = 0 and (5 + b)/2 = 2,
a = 4, b = -1.

So Q(4, -1).