#
Section 12-3

#
Midpoint of a Line Segment

Suppose you are given two points in the plane (
*
x
*
_{
1
}
,
*
y
*
_{
1
}
) and (
*
x
*
_{
2
}
,
*
y
*
_{
2
}
), and asked to find the point halfway between them. The coordinates of this
midpoint
will be:

An easy way to think about this is that the
*
x
*
-coordinate of the midpoint is the average of the
*
x
*
-coordinates of the two points, and likewise with the
*
y
*
-coordinate.

Example:

Find the midpoint between (–2, 5) and (7, 7).

Use the formula. The coordinates of the midpoint are:

Simplify.