OBJECTIVE 7 Use the midpoint formula.If the coordinates of the endpoints
of a line segment are known, then the coordinates of the midpointof the segment can
be found.
FIGURE 10shows a line segment PQwith endpoints and Ris
the point with the same x-coordinate as Pand the same y-coordinate as Q. So the co-
ordinates of Rare 1 - 8, - 22.
P 1 - 8, 42 Q 1 3, - 22.
142 CHAPTER 3 Graphs, Linear Equations, and Functions
yx
0P(–8, 4)MR(–8, –2) Q(3, –2)
–4–442FIGURE 10The x-coordinate of the midpoint Mof PQis the same as the x-coordinate of the
midpoint of RQ. Since RQis horizontal, the x-coordinate of its midpoint is the
averageof the x-coordinates of its endpoints.
The y-coordinate of Mis the average of the y-coordinates of the midpoint of PR.
The midpoint of PQis M 1 - 2.5, 12 .This discussion leads to the midpoint formula.
1
2
14 + 1 - 222 = 1
1
2
1 - 8 + 32 = -2.5
Midpoint FormulaIf the endpoints of a line segment PQare and its midpoint Mis
a
x 1 x 2
2
,
y 1 y 2
2
b.
1 x 1 , y 12 1 x 2 , y 22 ,
The small numbers 1 and 2 in the ordered pairs above are called subscripts.Read
as “x-sub-one,y-sub-one.”
Finding the Coordinates of a MidpointFind the coordinates of the midpoint of line segment PQwith endpoints
and
Use the midpoint formula with and
MidpointNOW TRYa
4 + 6
2
,
- 3 + 1 - 12
2
b = a
10
2
,
- 4
2
b = 15 , - 22
x 1 = 4 ,x 2 = 6 ,y 1 = - 3 , y 2 = - 1.
Q 1 6, - 12.
P 1 4, - 32
EXAMPLE 6
1 x 1 , y 12
NOW TRY
EXERCISE 6
Find the coordinates of the
midpoint of the line segment
PQwith endpoints P
and Q.
NOW TRY ANSWER
- 1 - 1, 1 2