Unformatted text preview: Move T: slope of QS
1 x 2 and y
slope of QW
4
2
4
2 1y
¬5 x
1y
¬5 x 3
( 3)
2
7 4 slope of CD slope of TW y 3.
slope of ST
y ¬x
y ¬x 3. Move W: slope of QS slope of TW 2
7
2
7 y ¬x
y ¬x ( 2)
( 1)
2
1 Again, x
8 and y 0.
slope of QW slope of ST
y
x 3
( 3)
y3
x3 ¬2
1 ¬5
7 4
1 ¬1
6 36. y 1
4 Q ¬3
5 R x
8 and y 0.
So, move W to ( 8, 0).
35. slope of AB For (10, 0) and ( 2, 2), CD AB.
slope of BC ¬2
Suppose D is ( 2, 2).
slope of DA ¬ 4 ( 2)
1 ( 2)
¬2
So DA BC.
So, ( 2, 2), (4, 10), and (10, 0) are the
possibilities for the fourth vertex. Any of these
values results in both pairs of opposite sides being
parallel, and thus, the four points form a
parallelogram. 1
4
1
4 Again, x 2 and y
So, move T to (2, 3) ( 1)
x4
y1
x4 x O S y B The fourth vertex can have one of three possible
positions to complete the parallelogram.
Let T(x, y) be the fourth vertex.
Find the slopes of ST and RT so that they equal
those of QR and QS, respectively.
slope of ST slope of QR A x O C y
x The fourth vertex can have one of three possible
positions to complete the parallelogram.
Let D(x, y) be the fourth vertex.
Find the slopes of BD and CD so that they equal
those of AC and AB, respectively.
slope of BD slope of AC
y
x
y
x 5
7
5
7 1 ¬4 1 Suppose T is (2, 4
1 slope of RT slope of RS 1 ¬1
1 1
1 ¬1 slope of RT ¬ 0
4 2
( 2) ¬1
So QT RS . 5
7 y
x
y
x ¬2
Suppose D is (4, 10).
4
1 ¬2
So AD BC. Chapter 8 1
1 Suppose T is ( 4, 0). So AB CD. slope of AD 2 ¬1
slope of QT ¬ 10
4 2). ¬2 So QS RT. ¬ 0 ( 1)
10 4
¬1
6
4 ( 2) ¬3 Suppose D is (10, 0). slope of BC ¬ 31 ¬3 ¬5
3
7
¬1
6 ¬ 1 1 ( 22) For (2, 2) and ( 4, 0), ST QR.
12
slope of QS ¬ For (10, 0) and (4, 10), BD AC.
slope of AB ¬ 5 4 slope of CD ( 1)
( 1)
y1
x1 254 1
1
1
1 slope of QS
¬ 1 1 ( 22)
¬ 13 ...
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Slope, Trigraph

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