32.
L
is on
PN
and
M
is on
RN
so graph
N
,
P
, and
R
and extend
PN
and
RN
so that
PR
divides
NL
and
MN
.
P
L
N
P
2
1
, and
PR
divides
NL
and
MN
proportionally so
M
RN
R
2
1
. Then
LP
2(
PN
)
and
MR
2(
RN
). Starting at
N
(8, 20), move to
P
(11, 16) by moving down 4 units and then right
3 units. Locate
L
by moving from
P
down 8 units
and then right 6 units. The coordinates of
L
are
(17, 8). Now starting at
N
(8, 20), move to
R
(3, 8)
by moving down 12 units and then left 5 units.
Locate
M
by moving from
R
down 24 units and
then left 10 units. The coordinates of
M
are
(
7,
16).
Verify that
LP
2(
PN
) and
MR
2(
RN
).
PN
¬
(11
8)
2
(16
20)
2
¬
9
16
¬
25 or 5
LP
¬
(11
17)
2
(16
8)
2
36
64
100 or 10
So,
LP
2(
PN
).
RN
(8
3)
2
(20
8)
2
25
144
169 or 13
MR
[3
(
7)]
2
[8
(
16)]
2
100
576
676 or 26
So,
MR
2(
RN
).
33.
To find
x
:
The sides of the large triangle are cut in equal
parts by the segment whose length is labeled
x
2, so this segment is a midsegment and its
length is half the length of the segment whose
length is labeled
5
3
x
11.
x
2
¬
1
2
5
3
x
11
x
2
¬
5
6
x
1
2
1
1
6
x
2
¬
1
2
1
1
6
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Harshad number, Trigraph, pn, PR divides

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