Graphs, Equations, And Inequalities Worksheets Page 5
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11B5
Appendix B.1
The Cartesian Plane
The Midpoint Formula
To find the midpoint of the line segment that joins two points in a coordinate plane,
find the average values of the respective coordinates of the two endpoints using the
Midpoint Formula.
The Midpoint Formula
The midpoint of the line segment joining the points
x
, y
and
x
, y
is given by
1
1
2
2
the Midpoint Formula
x
x
y
y
1
2
1
2
Midpoint
,
.
2
2
Example 5
Finding a Line Segment’s Midpoint
y
Find the midpoint of the line segment joining the points
5,
3
and
9, 3 .
Solution
6
(9, 3)
Let
x
, y
5,
3
and
x
, y
9, 3 .
1
1
2
2
3
(2, 0)
x
x
y
y
1
2
1
2
Midpoint
,
x
Midpoint Formula
2
2
− 6
− 3
3
6
9
−3
5
9
3
3
(− 5, − 3)
Midpoint
,
Substitute for
x
, y
, x
,
and
y
.
1
1
2
2
2
2
−6
2, 0
Simplify.
Figure B.9
The midpoint of the line segment is
2, 0 ,
as shown in Figure B.9.
.
Now try Exercise 59
Estimating Annual Revenues
Example 6
Verizon Communications had annual revenues of $88.1 billion in 2006 and
$97.4 billion in 2008. Without knowing any additional information, what would you
estimate the 2007 revenue to have been?
(Source: Verizon Communications)
Solution
One solution to the problem is to assume
Verizon Communications
Annual Revenues
that revenue followed a linear pattern. With
this assumption, you can estimate the 2007
98
(2008, 97.4)
revenue by finding the midpoint of the line
97
segment connecting the points
2006, 88.1
96
and
2008, 97.4 .
95
94
(2007, 92.8)
2006
2008
88.1
97.4
93
Midpoint
Midpoint
,
92
2
2
91
90
2007, 92.8
89
(2006, 88.1)
88
So, you would estimate the 2007 revenue to
have been about $92.8 billion, as shown in
2006
2007
2008
Figure B.10. (The actual 2007 revenue was
Year
$93.5 billion.)
Figure B.10
.
Now try Exercise 65
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