Prove that if a line L 1 with slope m 1 is perpendicular to a line L 2 with slope m 2 , then m 1 m 2 = − 1 . Hint: Refer to the accompanying figure. Show that m 1 = b and m 2 = c . Next, apply the Pythagorean Theorem and the distance formula to the triangles O A C , O C B , and O B A to show that 1 = − b c .
Prove that if a line L 1 with slope m 1 is perpendicular to a line L 2 with slope m 2 , then m 1 m 2 = − 1 . Hint: Refer to the accompanying figure. Show that m 1 = b and m 2 = c . Next, apply the Pythagorean Theorem and the distance formula to the triangles O A C , O C B , and O B A to show that 1 = − b c .
Solution Summary: The author explains that the slope of two perpendicular lines is equal to -1.
Prove that if a line
L
1
with slope
m
1
is perpendicular to a line
L
2
with slope
m
2
, then
m
1
m
2
=
−
1
.
Hint: Refer to the accompanying figure. Show that
m
1
=
b
and
m
2
=
c
. Next, apply the Pythagorean Theorem and the distance formula to the triangles
O
A
C
,
O
C
B
,
and
O
B
A
to show that
1
=
−
b
c
.
Elementary Algebra For College Students (10th Edition)
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