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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 the given points
(
2
,
−
1
)
,
(
0
,
2
)
and
(
3
,
2
)
.
A
Collinear
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B
Non-collinear
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C
Exists on parallel lines
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D
Exists on perpendicular lines
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Solution
The correct option is
B
Non-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
1
)
+
x
3
(
y
1
−
y
2
)
|
Here the points are
(
2
,
−
1
)
,
(
0
,
2
)
and
(
3
,
2
)
, therefore, the area of the triangle is:
A
=
1
2
|
2
(
2
−
2
)
+
0
(
2
+
1
)
+
3
(
−
1
−
2
)
|
⇒
A
=
1
2
|
2
(
0
)
+
0
(
3
)
+
3
(
−
3
)
|
⇒
A
=
1
2
|
−
9
|
⇒
A
=
9
2
≠
0
Since the area of the triangle is not zero,
Hence, the points are non-collinear.
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Condition of Concurrency of 3 Straight Lines
Standard XII Mathematics
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