Preparing for the Regents Examination Geometry, AK

d Slope parallel 2 _
5
Slope perpendicular 5 _
e Slope parallel 9 _
10
Slope perpendicular 10 _
9
f Slope parallel 13
Slope perpendicular 1 _
13
4 a Perpendicular; slopes are negative
reciprocals
b Perpendicular; slopes are negative
reciprocals
c Neither; slopes are neither equal nor
negative reciprocals
d Neither; slopes are neither equal nor
negative reciprocals
e Perpendicular; lines with a slope of 0 are
perpendicular to lines with no slope
f Parallel; slopes are the same
5 a Yes
b Yes
c No
6 a y 1 _ x
4 17 _
4
b y 2x 7
c y 1 _ x 4
5
7 a Right triangle
b Not a right triangle
8-4 The Midpoint of a Line
Segment
(pages 153–154)
1 (2) (1.5, 1)
2 (4) (2.5, 2)
3 (2) (2, 0.1)
4 (1) (8, 0)
5 (4) (17, 20)
6 (4) (13, 13)
7 (5a, 5r)
8 (3x, 5y)
9 (10, 11)
2
10
y
8
7
6
5
4
3
2
G
1
8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
D
L
A
A rectangle is formed.
M GL (0, 1), M LA (2, 1), M DA (2, 3),
M GD (0, 3)
11 (0, 2)
12 a −−
BD is parallel to −−
EF because their slopes
are 3 _ .
4
b EF 1 _ BD
2
5 1 _ (10)
2
5 5
13 a m 5 _
2
b m 2 _
5
5
c M ( 4, _
2 )
d y 5 _ x
6 35 _
6
14 y 4x 9
15 y 1 _ x
5 4 _
5
8-5 Coordinate Proof
(pages 163–165)
1 The triangle is an isosceles triangle because
WI WN √ 40 .
2 Slopes of −−−
NA and −−−
AQ are negative reciprocals
proving these two lines form a right
angle by being perpendicular; therefore,
NAQ is a right triangle.
3 AM CM BM √ 26 ; the midpoint of the
hypotenuse is equidistant from all three
vertices.
4 The slopes are negative reciprocals so the
median is also the altitude.
x
8-5 Coordinate Proof 41