Preparing for the Regents Examination Geometry, AK

14
15
b C(3, 5), A(4, 7), R(7, 4)
c C(5, 3), A(7, 4), R(4, 7)
d c
D"
D'''
I"
K"
2
1
K'
11109 8 7 6 5 4 3 2 1
1
I'''
2
K'''
3
4
5
1 2 3 4 5 6 7 8
y
12
11
10
9
8
7
6
5
4
3
I
K
D
I'
D'
9 10 11
a K(6, 1), I(9, 2), D(10, 7)
b K(6, 1), I(9, 2), D(10, 7)
c K(1, 2), I(4, 1), D(5, 4)
10
9
8
7
6
A"
R'''
5
4
3
R"
A'''
2
1
J'''
J"
J' J
109 8 7 6 5 4 3 2 1
1
2
3
1 2 3 4
A'
R'
5 6 7
A
8 9 10
4
5
R
a J(1, 0), A(3, 1), R(2, 2)
b J(0, 2), A(2, 6), R(4, 4)
c J(2, 0), A(6, 2), R(4, 4)
6-8 Composition of
Transformations
(pages 117–119)
1 (3) R 200
2 (2) ___
AT
3 (1) (x, y)
4 (3) r y x D 3
5 (1) a direct isometry
6 (2) (x, y)
7 (4) (3, 8)
8 (4) D
9 (3) T 4, 0
10 (1) (x, y)
11 (3) orientation
12 N
y
x
x
13 A
14 R 90
15 Any combination of three rotations, the sum
of whose angles is 100
16 Any combination of two rotations, the sum
of whose angles is 180
17 Glide reflection
18 (6, 1)
19 (2, 3)
20 (2, 7)
21
y
22
10
9
8
7
P'
M
y x
6
5
M'
4
3
P
2
C
1
C'
109 8 7 6 5 4 3 2 1
1
C"
2
3
4
1 2 3 4 5 6 7 8 9 10
M"
5
6
7
P"
8
9
10
C(2, 1), M(7, 5), P(4, 8)
C(2, 1), M(7, 5), P(4, 8)
d r y x
Y'
10
9
8
7
6
5
Y
X"
X
4
3
2
X'
Z'
1
Z
109 8 7 6 5 4 3 2 1
1
1 2 3 4 5 6 7 8 9 10
2
3
4
5
Y"
y x
6
7
8
9
10
Z"
X(5, 3), Y(2, 6), Z(7, 1)
X(3, 5), Y(6, 2), Z(1, 7)
d (1) rotation
Chapter Review (pages 119–121)
1 (1) I
2 (1) WOW
3 (3) parallel to the y-axis
4 (3) (5, 2)
y
Chapter Review 33
x
x