Linear Functions Worksheet Page 5
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3860
Chapter 1 LINEAR FUNCTIONS
5
: The desired line has a
This line has a slope of
38. Two lines are perpendicular if the product of their
2
2
slope of ¡
slopes is ¡1:
since it is perpendicular to the given
5
The slope of the diagonal containing (4; 5) and
line. Use the de…nition of slope.
(¡2; ¡1) is
y
¡ y
2
1
m =
5 ¡ (¡1)
6
x
¡ x
m =
=
= 1:
2
1
4 ¡ (¡2)
6
2 ¡ (¡1)
=
k ¡ 4
The slope of the diagonal containing (¡2; 5) and
2
2 + 1
¡
=
(4; ¡1) is
5
k ¡ 4
¡2
3
5 ¡ (¡1)
6
=
m =
=
= ¡1:
5
k ¡ 4
¡2 ¡ 4
¡6
¡2(k ¡ 4) = (3)(5)
The product of the slopes is (1)(¡1) = ¡1; so the
¡2k + 8 = 15
diagonals are perpendicular.
¡2k = 7
7
39. The line goes through (0; 2) and (¡2; 0)
k = ¡
2
2 ¡ 0
2
m =
=
= 1
0 ¡ (¡2)
2
37. A parallelogram has 4 sides, with opposite sides
parallel. The slope of the line through (1; 3) and
The correct choice is (a).
(2; 1) is
40. The line goes through (1; 3) and (2; 0):
3 ¡ 1
2
m =
=
= ¡2:
3 ¡ 0
3
1 ¡ 2
¡1
m =
=
= ¡3
1 ¡ 2
¡1
¡
¢
¡
¢
5
7
¡
; 2
¡
; 4
The slope of the line through
and
The correct choice is (f).
2
2
is
41. The line appears to go through (0; 0) and (¡1; 4):
2 ¡ 4
¡2
¡
¢ =
m =
= ¡2:
5
7
1
¡
¡
¡
4 ¡ 0
4
2
2
m =
=
= ¡4
¡1 ¡ 0
¡1
Since these slopes are equal, these two sides are
42. The line goes through (¡2; 0) and (0; 1):
parallel.
¡
¢
7
¡
; 4
and (1; 3) is
The slope of the line through
2
1 ¡ 0
1
m =
=
0 ¡ (¡2)
2
4 ¡ 3
1
2
m =
=
= ¡
:
7
9
9
¡
¡ 1
¡
2
2
43. (a) See the …gure in the textbook.
Segment MN is drawn perpendicular to segment
¡
¢
P Q: Recall that M Q is the length of segment M Q:
5
¡
; 2
and (2; 1) is
Slope of the line through
2
4y
M Q
m
=
=
1
4x
P Q
2 ¡ 1
1
2
m =
=
= ¡
:
5
9
9
¡
¡ 2
¡
2
2
From the diagram, we know that P Q = 1: Thus,
MQ
m
=
; so M Q has length m
:
1
1
1
Since these slopes are equal, these two sides are
4y
¡QN
¡QN
parallel.
m
=
=
=
(b)
2
4x
P Q
1
Since both pairs of opposite sides are parallel, the
QN = ¡m
quadrilateral is a parallelogram.
2
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