Teaching Notes 4.15: Using the Midpoint Formula
A midpoint is a point on a line segment that is equidistant from its endpoints. The midpoint
between (x 1 ,y 1 )and(x 2 ,y 2 ) can be found by using the midpoint formula:(
x 1 +x 2
2,
y 1 +y 2
2)
.
Although this formula seems relatively straightforward, students may replace the variables with
the wrong value, resulting in an incorrect midpoint.SPECIAL MATERIALS:
Graph paper, rulers- Explain that a midpoint is the point on a line segment that divides the segment into two
equal parts. It is written as an ordered pair. - Present the midpoint formula and relate it to averages. To find the average of two numbers,
you must add the numbers and divide by two. The average of these numbers is the number
exactly between the two numbers being averaged. Similarly, the midpoint formula takes the
average of thex-coordinates and the average of they-coordinates of the two ordered pairs. - Review the steps for finding the midpoint and the example on the worksheet with your stu-
dents. Explain that students must label the ordered pairs as (x 1 ,y 1 )or(x 2 ,y 2 ) in the problem
and correctly replace each variable with the appropriate value. Ask your students to ver-
ify that (4, 5) is the midpoint by graphing this point and the segment whose endpoints are
(2, 3) and (6, 7) on graph paper.
EXTRA HELP:
Rewrite the formula with the appropriatex-andy-coordinates before you solve. Taking this extra
step will help eliminate careless mistakes.ANSWER KEY:
(1)(
3
1
2
,4
1
2
)
(2)(3, 5) (3)(1, 3) (4)
(
1,− 1
1
2
)
(5)(−6,−2) (6)
(
1
2
,− 3
)
(7)(2, 7) (8)
(
1
2
,3
1
2
)
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(Challenge)The missingx-coordinate is 9.
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