Graphs, Equations, And Inequalities Worksheets Page 9
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11B9
Appendix B.1
The Cartesian Plane
32.
Meteorology
The table shows the lowest temperature
Verifying a Polygon
In Exercises 47– 54, show that the
on record (in degrees Fahrenheit) in Flagstaff, Arizona
y
points form the vertices of the polygon.
for each month
x,
where
x
1
represents January.
47. Right triangle:
4, 0 , 2, 1 ,
1,
5
(Source: U.S. National Oceanic and Atmospheric
1, 3 , 3, 5 , 5, 1
48. Right triangle:
Administration)
49. Isosceles triangle:
1,
3 , 3, 2 ,
2, 4
50. Isosceles triangle:
2, 3 , 4, 9 ,
2, 7
Month, x
Temperature, y
51. Parallelogram:
2, 5 , 0, 9 ,
2, 0 , 0,
4
1
22
52. Parallelogram:
0, 1 , 3, 7 , 4, 4 , 1,
2
2
23
53. Rectangle:
5, 6 , 0, 8 ,
3, 1 , 2, 3
(Hint: Show
3
16
that the diagonals are of equal length.)
4
2
54. Rectangle:
2, 4 , 3, 1 , 1, 2 , 4, 3
(Hint: Show that
5
14
the diagonals are of equal length.)
6
22
7
32
Finding a Line Segment’s Midpoint
In Exercises 55–64,
8
24
(a) plot the points, (b) find the distance between the
9
23
points, and (c) find the midpoint of the line segment
10
2
joining the points.
11
13
55.
0, 0 , 8, 6
12
23
56.
1, 12 , 6, 0
57.
4, 10 , 4,
5
Finding a Distance
In Exercises 33–42, find the distance
58.
7,
4 , 2, 8
between the points algebraically and confirm graphically
by using centimeter graph paper and a centimeter ruler.
59.
1, 2 , 5, 4
60.
2, 10 , 10, 2
33.
6,
3 , 6, 5
34.
3, 0 ,
3,
7
1
5
4
61.
, 1 ,
,
35.
3,
1 , 2,
1
36.
11, 4 ,
1, 4
2
2
3
1
1
1
1
62.
,
,
,
37.
2, 6 , 3,
6
3
3
6
2
63.
6.2, 5.4 ,
3.7, 1.8
38.
8, 5 , 0, 20
1
4
64.
16.8, 12.3 , 5.6, 4.9
,
, 2,
1
39.
2
3
2
5
40.
, 3 ,
1,
3
4
Estimating Annual Revenues
In Exercises 65 and 66, use
41.
4.2, 3.1 ,
12.5, 4.8
the Midpoint Formula to estimate the annual revenues (in
42.
9.5,
2.6 ,
3.9, 8.2
millions of dollars) for Texas Roadhouse and Papa John’s
in 2006. The revenues for the two companies in 2003 and
Verifying a Right Triangle
In Exercises 43– 46, (a) find
2009 are shown in the tables. Assume that the
the length of each side of the right triangle and (b) show
revenues followed a linear pattern.
(Sources: Texas
that these lengths satisfy the Pythagorean Theorem.
Roadhouse, Inc.; Papa John’s International)
y
y
43.
44.
65. Texas Roadhouse
(4, 5)
5
4
8
Annual revenue
(13, 5)
Year
3
(in millions of dollars)
(1, 1)
4
(1, 0)
2
(4, 1)
2003
287
1
x
4
8
(13, 0)
2009
942
x
1
2
3
4
5
y
y
45.
46.
66. Papa John’s Intl.
(1, 5)
6
4
(9, 4)
Annual revenue
4
Year
2
(5, − 2)
(in millions of dollars)
2
(9, 1)
x
x
2003
917
(− 1, 1)
6
8
6
(1, − 2)
2009
1106
− 2
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