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Byju's Answer
Standard XII
Mathematics
Condition of Concurrency of 3 Straight Lines
Find the corr...
Question
Find the correct option regarding given points
(
1
,
2
)
,
(
2
,
4
)
and
(
3
,
6
)
A
Non-colllinear
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B
Exists on parallel lines
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C
Collinear
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D
Exists on perpendicular lines
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Solution
The correct option is
B
Collinear
Area of the triangle with vertices
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
is:
A
=
1
2
|
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
2
)
+
x
3
(
y
1
−
y
2
)
|
Here the points are
(
1
,
2
)
,
(
2
,
4
)
and
(
3
,
6
)
, therefore, the area of the triangle is:
A
=
1
2
|
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
|
A
=
1
2
|
1
(
4
−
6
)
+
2
(
6
−
2
)
+
3
(
2
−
4
)
|
⇒
A
=
1
2
|
1
(
−
2
)
+
2
(
4
)
+
3
(
−
2
)
|
⇒
A
=
1
2
|
−
2
+
8
−
6
|
⇒
A
=
1
2
|
−
8
+
8
|
⇒
A
=
0
Since the area of the triangle is zero,
Hence, the points are collinear.
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Condition of Concurrency of 3 Straight Lines
Standard XII Mathematics
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