TUTORIALS:

Midpoint of a Line Segment
Objective Learn the algebraic formula for the
midpoint of a line segment, whose endpoints are given by ordered
pairs of numbers.
This is a relatively straightforward lesson, which shows that
the x and ycoordinates of the midpoint of a line segment can be
obtained by taking the averages of the x and ycoordinates,
respectively.
Begin by reembering the formula for the average of two numbers
x and y.
Take a look at the following diagram.
The average is the midpoint of the segment
between the two points, or the halfway point between x and y.
Two points in a plane have coordinates (x_{ 0} , y_{
0}) and (x_{ 1} , y_{ 1}). How can we find
the coordinates of the midpoint of the segment joining them?
For two points in a plane, the halfway point between them
should have an xcoordinate that is halfway between the
xcoordinates of the two points. This is shown in the diagram
below.
In the same way, the ycoordinate of the midpoint is the
midpoint of the ycoordinates. The formula for the ycoordinate
of the midpoint is . This is shown in the diagram below.
The formula for the coordinates of the midpoint of a line
segment is given below.
Definition of Midpoint
The midpoint of the segment joining two points at (x_{ 0}
, y_{ 0}) and (x_{ 1} , y_{ 1}) is given
by
Now you should practice using the formula to find midpoints of
line segments.
Exercises
Find the coordinates of the midpoint of a segment with each
pair of endpoints.
1. A (9, 4), B (7, 6) (8, 5)
2. L (8, 2), M (0, 10) (4, 4)
3. X (2, 5), Y ( 6, 3) ( 2, 4)
4. T (1, 9), U (4, 7) (2.5, 1)
