Preparing for the Regents Examination Geometry, AK

16 (4) 4
17 (1) 90 x
18 8
19 x 3, PD 6, RP 12, RD 18
20 x 2, y 4, BE 9, AD 12
Note: For exercises 21–24, check students’
sketches.
21 Two concentric circles. Locus: radius 1 and
radius 7.
22 Circle, radius 3, x 2 y 2 9. Two lines,
x 4, x 4. Locus: 0 points
23 Circle: x 2 y 2 4. Circle: x 2 (y 4) 2 9.
Locus: 1 point, (0, 2)
24 Two lines parallel to line m on opposite sides
and 4 centimeters from m. Circle with center
H and radius 2. Locus: 1 point
25 (x 4) 2 (y 2) 2 1
26 y x 4
27 Two lines: y x 2 and y x 2
Note: For exercises 28–37, check students’
sketches.
28 b (2, 0.5), (5, 1), (1, 1)
2
c y _ x
2x
6 _
1
3 _
6
29 b (5, 7), (1, 3), (3, 1)
2
y
c x _
3y
8 _
1
4 _
8
30 b (2, 0), (2, 2), (6, 2)
x 2
c y
_
x
8 _
2 1 _
2
31 b (1, 0), (1, 4), (1, 4)
y 2
c x _ 1
8
32 (0, 5), (3, 4), (3, 4)
33 (0, 5), (3, 8)
34 (0, 3), (3, 9)
35 (2 √ 7 , 1 √ 7 ), (2
36 (3, 10), (1, 6)
√ 7 , 1 √ 7 )
37 (0, 4), ( √ 7 , 3), ( √ 7 , 3)
38 The intersection of the perpendicular bisector
of AB, and circle with A as center
Case I x 1 _ f (0 points)
2
Case II x 1 _ f (1 point)
2
Case III x 1 _ f (2 points)
2
39 The intersection of one circle with radius of
2.5, concentric with the given circles, and
two lines parallel to the given line, one on
each side at a distance x from the given line.
Case I x 2.5 (4 points)
Case II x 2.5 (2 points)
Case III x 2.5 (0 points)
40 The intersection of circle with center P
and radius d and circle with center Q and
radius d.
Case I x 2d (2 points)
Case II x 2d (1 point)
Case III x 2d (0 points)
41 The intersection of two lines parallel to line
m, one on each side at a distance d from line
m and the circle with center A and radius r.
Case I r d (0 points)
Case II r d (2 points)
Case III r d (4 points)
42 Locus: A line parallel to the north side and
south side of the courtyard and midway
between them. Since the width of the garden
is 60 ft, every point on this line will be equidistant
from the north and south walls and
at least 30 feet from the North Entrance.
43 Check students’ constructions of the orthocenter
of an acute triangle.
44 Check students’ constructions of the perpendicular
bisector of the three sides of a right
triangle.
45 Check students’ constructions of a circle that
passes through the three vertices of an obtuse
triangle.
Chapter Review 91