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Joint Entrance Examination
Mathematics
Straight Lines and Pair of Straight Lines
Question 193
Question 193 of 303
Easy
MCQ
The points
(
0
,
8
3
)
,
(
1
,
3
)
\left(0,\dfrac83\right),\ (1,3)
(
0
,
3
8
)
,
(
1
,
3
)
and
(
82
,
30
)
(82,30)
(
82
,
30
)
:
A
form an acute angled triangle.
B
form a right angled triangle.
C
lie on a straight line.
D
form an obtuse angled triangle.
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Official solution
Slope from
(
0
,
8
3
)
\left(0,\dfrac83\right)
(
0
,
3
8
)
to
(
1
,
3
)
(1,3)
(
1
,
3
)
:
3
−
8
3
=
1
3
3-\dfrac83=\dfrac13
3
−
3
8
=
3
1
. Slope from
(
1
,
3
)
(1,3)
(
1
,
3
)
to
(
82
,
30
)
(82,30)
(
82
,
30
)
:
30
−
3
82
−
1
=
27
81
=
1
3
\dfrac{30-3}{82-1}=\dfrac{27}{81}=\dfrac13
82
−
1
30
−
3
=
81
27
=
3
1
. Same slope through common point
(
1
,
3
)
(1,3)
(
1
,
3
)
: all three points are collinear.
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