Preparing for the Regents Examination Geometry, AK

14 The distance from A to B is
√
[2 (7) ] 2 (5 1 ) 2
5 2 4 2 41 . The distance from B to C
is √
[3 (2) ] 2 (1 5 ) 2
5 2 4 2 41 . The distance from C to D
is
√
[(2) 3 ] 2 [(3) 1 ] 2
5 2 4 2 41 . The distance from D to A
is √
[(7) (2)] 2 [(1 (3)] 2
5 2 4 2 41 . The perimeter of ABCD
41 41 41 41 4 41 .
15 The length of the base ___
AC is the difference
between the x-coordinates of A and C;
6 (4) 10. The height is the vertical distance
from B to ___
AC or the difference between
the y-coordinates; 6 (6) 12. Therefore,
A 1 _ bh
2 1 _ (10)(12) 60.
2
16 Using the distance formula, AB BC 13
and CA 10. The perimeter of ABC
13 13 10 36.
17 Isosceles because PA AT 5
18 Scalene because AB √ 53 , CB √ 74 , and
AC √ 29
19 Scalene because MA √ 130 , AD √ 26 ,
and MD √ 104
20 Scalene because WI √ 26 , IT √ 125 , and
WT √ 109
21 All three sides measure 2, therefore the triangle
must be equilateral.
22 The radius is the distance from the center to
any point on the circle.
r √
(4 1 ) 2 (2 2 ) 2 5
Diameter 2(5) 10
23 The two diagonals are congruent because
AD CB 2.
24 A B 2 [(1) 3 ] 2 (2 2 ) 2 32
B C 2 (3 1 ) 2 (2 4 ) 2 8
A C 2 [(1) 1 ] 2 [(2) 4 ] 2 40.
32 8 40 or A B 2 B C 2 A C 2 .
6-2 Translations
(pages 94–95)
1 (1) (1, 2)
2 (2) (3, 2)
3 (4) T 8, 4
4 (4) 6
5 T 0, 2
6 T 3, 0
7 (4, 1)
8 (3, 7)
9 (2, 4)
10 (4, 3)
11 (4, 2)
12 (2, 2)
13 T 3, 2
14 T 2, 2
15 (3, 0)
16 (7, 3)
17 (4, 7)
18 K(8, 5) → (2, 9), E(10, 3) → (4, 1),
N(2, 2) → (8, 6)
19
y
20
D
10
9
8
7
D"
6
5
4
3 W"
D'
2
1
W
5 4 3 2 1
1
2
3
4
5
1 2 3 4
W'
5 6 7 8 9 10
E
E'
E"
a D’(1, 2), E’(6, 3), W’(2, 1)
b D(0, 6), E(7, 7), W(3, 3)
c T 3, 1
A'
W'
y
10
9
8
7
6
5
4
3
2
1
5 4 3 2 1 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
S'
S(3, 4)
H'
A"
A(0, 1)
W"
W(1, 2)
S"
H(5, 1)
a W’(2, 0), A’(3, 3), S’(0, 6), H’(2, 3)
b W(5, 1), A(4, 2), S(7, 5), H(9, 2)
c T 4 , 1
H"
x
x
6-2 Translations 29