Preparing for the Regents Examination Geometry, AK

18 Two lines, one on each side, parallel to the
given line and at a distance r from the given
line
19 One line parallel to the two parallel lines and
midway between them
20 The diameter of the circle that is the perpendicular
bisector of the given chord
21 The diameter of the circle that is the perpendicular
bisector of the given chord
22 A ray that is the angle bisector
23 A line perpendicular to the point on the
given line
24 The perpendicular bisector of the chord that
joins the two given points
Locus in the Coordinate Plane
(Pages 418–419)
1 (4) y 2 or y 2
2 (1) x 2
3 (2) x 5
4 (2) y 1
5 (4) (x 1) 2 (y 3) 2 25
6 (3) y 3 and x 0
7 (4) y x 1 and y x 5
8 y 1
9 y 2, y 10
10 y 4
11 y x 3 and y x 3
12 y x 3
13 x 1 and y 0
14 a (x 1) 2 (y 4) 2 16
b x 2 y 2 36
c x 2 (y 1) 2 9
d (x 1) 2 y 2 1
e x 2 (y 2) 2 6.25
f (x 1) 2 (y 3) 2 30.25
15 The showers could be placed anywhere on
the perpendicular bisector of the line segment
joining the diving boards, which is
35 ft from each of the diving boards.
14-5 Compound Locus and
the Coordinate Plane
(pages 421–422)
1 (3) a pair of points
2 (4) the empty set
3 (1) 0
4 (3) a pair of points
5 (3) 2
6 (2) 1
7 a 4 b 2 c 0
8 Find the point of concurrency (circumcenter)
of the perpendicular bisectors of the sides of
the triangle formed.
9 3
10 2
11 Parallel lines 2 inches from the given line,
one on each side
a Circle with radius 3, center R. 1 point
b Circle with radius 6, center R. 2 points
c Circle with radius 7, center R. 3 points
d Circle with radius 9, center R. 3 points
12 For all parts, check students’ sketches.
a Two intersecting circles, but not tangent.
2 points
b Two tangent circles. 1 point
c Two disjoint circles. 0 points
13 Sketch circle and two lines; 4 points.
14 Sketch a line and a circle; 2 points.
15 Sketch two lines bisecting vertical angles,
and two parallel lines; 4 points.
16 Sketch two concentric circles and two lines
bisecting vertical angles; 8 points.
17 The intersection of the line parallel to m and
k and midway between them, and a circle
with A as the center and d as the radius.
Case I d 1 _ f (0 points)
2
Case II d 1 _ f (1 point)
2
Case III d 1 _ f (2 points)
2
18 The intersection of the perpendicular
bisector of segment AB and a circle about
center A with radius x.
Case I Radius x 1 _ d (0 points)
2
Case II Radius x 1 _ d (1 point)
2
Case III Radius x 1 _ d (2 points)
2
Compound Loci and the Coordinate Plane
(pages 423–424)
1 (4) 4
2 (3) 2
3 (4) 4
4 a 2 b 1 c 0
14-5 Compound Locus and the Coorinate Plane 89