32.
USING STRUCTURE Determine whether the statements are true or false. Explain your reasoning. DAEHF
B
C
a.
B
is between
A
and
C
.
b.
C
is between
B
and
E
.
c.
D
is between
A
and
H
.
d.
E
is between
C
and
F
.
33. ERROR ANALYSIS Describe and correct the error in
34. ERROR ANALYSIS Describe and correct the error in
4).
AB
=
(6
−
1)
2
+
[2
−
(
−
4)]
2
=
5
2
+
6
2
=
25
+
36
=
61
✗
35.
MODELING WITH MATHEMATICS
The
fi
gure shows
the position of three players during part of a water
polo match. Player A throws the ball to Player B,
who then throws the ball to Player C.
x
y
8
4
0
16
12
8
4
0
16
12
24
28
20
Distance (m)
Distance (m)
(18, 7)
(24, 14)
(8, 4)
Player A
Player B
Player C
a.
How far did Player A throw the ball? Player B?
b.
How far would Player A have to throw the ball to
throw it directly to Player C?

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18
Chapter 1
Basics of Geometry
36.
MODELING WITH MATHEMATICS
Your school is
20 blocks east and 12 blocks south of your house.
The mall is 10 blocks north and 7 blocks west of
your house. You plan on going to the mall right after
school. Find the distance between your school and the
mall assuming there is a road directly connecting the
school and the mall. One block is 0.1 mile.
37.
MATHEMATICAL CONNECTIONS
Point
S
is between
points
R
and
T
on
—
RT
. Use the information to write an
equation in terms of
x
. Then solve the equation and
fi
nd
RS
,
ST
,
and
RT
.
a.
RS
=
2
x
+
10
b.
RS
=
3
x
−
16
ST
=
x
−
4
ST
=
4
x
−
8
RT
=
21
RT
=
60
c.
RS
=
2
x
−
8
d.
RS
=
4
x
−
9
ST
=
11
ST
=
19
RT
=
x
+
10
RT
=
8
x
−
14
38.
THOUGHT PROVOKING Is it possible to design a table where no two legs have the same length? Assume that the endpoints of the legs must all lie in the same plane. Include a diagram as part of your answer.
39.
MODELING WITH MATHEMATICS
You have to walk
from Room 103 to Room 117.
103
107
113
117
121
119
115
111
109
105
101
86 ft
22 ft
a.
How many feet do you travel from Room 103
to Room 117?
b.
You can walk 4.4 feet per second. How many
minutes will it take you to get to Room 117?
c.
Why might it take you longer than the time in
part
(b)?
40.
MAKING AN ARGUMENT Your friend claims there is an easier way to find the length of a segment than the Distance Formula when the x-coordinates of the endpoints are equal. He claims all you have to do is subtract the y-coordinates. Do you agree with his statement? Explain your reasoning.
41.
REASONING
You travel from City X to City Y. You
know that the round-trip distance is 647 miles. City Z, a
city you pass on the way, is 27 miles from City X. Find
the distance from City Z to City Y. Justify your answer.