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Mathematics
Problem
Let
k
k
k
and
p
p
p
be real numbers. The line
k
x
−
4
y
+
1
=
0
kx - 4y + 1 = 0
k
x
−
4
y
+
1
=
0
is parallel to
2
x
+
3
y
−
5
=
0
2x + 3y - 5 = 0
2
x
+
3
y
−
5
=
0
and simultaneously perpendicular to
3
x
+
p
y
+
4
=
0
3x + py + 4 = 0
3
x
+
p
y
+
4
=
0
. Which ordered pair
(
k
,
p
)
(k,p)
(
k
,
p
)
satisfies both conditions? a)
(
−
8
3
,
2
)
\left(-\dfrac{8}{3},2\right)
(
−
3
8
,
2
)
b)
(
8
3
,
2
)
\left(\dfrac{8}{3},2\right)
(
3
8
,
2
)
c)
(
−
8
3
,
−
2
)
\left(-\dfrac{8}{3},-2\right)
(
−
3
8
,
−
2
)
d)
(
8
3
,
−
2
)
\left(\dfrac{8}{3},-2\right)
(
3
8
,
−
2
)
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