27.
2
x
2
3
y
5
¬
2
9
2
3
y
5
¬
2
2
x
2
9
y
5
¬
}
2
3
}
x
1
3
The perpendicular segment from the point (2, 0)
to the line
y
5
}
2
3
}
x
1
3 appears to intersect the
line
y
5
}
2
3
}
x
1
3 at (0, 3). Use the Distance
Formula to find the distance between (2, 0) and
y
5
}
2
3
}
x
1
3.
d
5
¬
Ï
(
x
2
2
w
x
1
)
2
1
w
(
y
2
2
w
y
1
)
2
w
5
¬
Ï
(2
2
0
w
)
2
1
(0
w
2
3)
2
w
5
¬
Ï
2
2
1
(
w
2
3)
2
w
5
¬
Ï
13
w
The distance between the line
y
5
}
2
3
}
x
1
3 and the
point (2, 0) is
Ï
13
w
units.
28. Given:
,
is equidistant to
m.
n
is equidistant to
m.
Prove:
,
i
n
Paragraph proof:
We are given that
,
is
equidistant to
m
, and
n
is equidistant to
m
.By
definition of equidistant,
,
is parallel to
m
, and
n
is parallel to
m
.By definition of parallel lines,
slope of
,
5
slope of
m
,and slope of
n
5
slope of
m
.By substitution, slope of
,
5
slope of
n
. Then,
by definition of parallel lines,
,
i
n.
29.
It is everywhere equidistant from the ceiling.
30.
The plumb line will be vertical and will be
perpendicular to the floor. The shortest distance from
a point to the floor will be along the plumb line.
31.
a
5
3,
b
5
4,
c
5
6, (
x
1
,
y
1
)
5
(4, 6)
5
¬
5
¬
5
¬
}
3
5
0
}
or 6
32a.
32b.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus

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