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Unformatted text preview: To find y: 5. LW TS, so by the Triangle Proportionality
L
WS
Theorem, TR
L
RW . Substitute the known
measures.
3 8
3 y
2
5y ¬ WS
6 y 6(5) ¬3(WS)
30 ¬3(WS)
10 ¬WS
6. Use the Midpoint Formula to find the midpoints
of AB and AC.
D 10 E ( 2) 0 6
,2
2 4 ( 2) 0 , 2 6
2 slope of BC D(4, 3) 5y Entrance to Walkthrough
Walkthrough to Clay Rd.
880
1408 1
2 BC. Pages 312–315 Practice and Apply 14. MN YZ, so by the Triangle Proportionality
MY
NZ
Theorem, XM
XN . Substitute the known
measures.
MY
¬9
4
6
6(MY) ¬4(9)
6(MY) ¬36
MY ¬6
XY XM MY
4 6 or 10
15. MN YZ, so by the Triangle Proportionality
MY
NZ
Theorem, XM
XN . Substitute the known
measures.
10 2
¬t 1
2
t2
8(t 2) ¬2(t 1)
8t 16 ¬2t 2
6t 16 ¬2
6t ¬18
t ¬3 9
16 . Since the sides have proportional lengths, RN QP.
10. In order to show DB AE, we must show that
AB
BC .
8
2
20 or 5
12
25
AB
BC , so the sides do not have proportional 16. DE BC, so by the Triangle Proportionality
Theorem, DB
AD
measures. lengths and DB is not parallel to AE.
11. To find x:
20 5x ¬2x
20 ¬7x
14 ¬7x
2 ¬x Entrance to Walkthrough
Walkthrough to Clay Rd.
x
¬ 1760 880(1760) ¬1408x
1,548,800 ¬1408x
1100 ¬x
The distance from the entrance to the
Walkthrough along Woodbury Avenue is 1100
yards. MR
RQ
MR
RQ
MN
NP ED
DC
ED
DC
AB
BC
ED
DC 8 13. The streets form a triangle cut by a Walkthrough
that is parallel to the bottom of the triangle. Use
the Triangle Proportionality Theorem.
Talbot Rd.
Woodbury Ave. 9. MQ ¬MR RQ
12.5 ¬4.5 RQ
8 ¬RQ
MP ¬MN NP
25 ¬9 NP
16 ¬NP
In order to show RN QP, we must show that
MN
NP .
9
4.5
¬ 8 or 16
9
¬ 16
MN
Thus, MR
RQ
NP 4 ¬8
¬3 y 33
3 4 or 0
00
10 ( 4) or 0 1
2 , then DE ¬7y
3 8
3y E( 3, 3) Because the slopes of DE and BC are equal,
DE BC.
8. First, use the Distance Formula to find BC and
DE.
BC ¬ [10 ( 4)]2 (0 0)2
¬ 196 0
¬14
DE ¬ ( 3 4)2 (3 3)2
¬ 49 0
¬7
7
DE
1
14 or 2
BC
If DE
BC 2 12. To find x:
1
2
3x 2 ¬3x
1
3x 2 ¬ 4
1
3x ¬ 6
x ¬18
To find y: 7. If the slopes of DE and BC are equal, DE BC.
slope of DE ¬3y
5
¬2
¬5 24
AD 24(3)
72
4 6
6 169 EC
AE . Substitute the known ¬ 18
3
¬18(AD)
¬18(AD)
¬AD Chapter 6 ...
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Midpoint Formula

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