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Byju's Answer
Standard XII
Mathematics
Condition of Concurrency of 3 Straight Lines
If three poin...
Question
If three points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
,
(
x
3
,
y
3
)
lie on the same line, prove that
y
2
−
y
3
x
2
x
3
+
y
3
−
y
1
x
3
x
1
+
y
1
−
y
2
x
1
x
2
=
0
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Solution
Points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
,
(
x
3
,
y
3
)
are collinear
(
x
1
y
2
+
x
2
y
3
+
x
3
y
1
)
−
(
x
2
y
1
+
x
3
y
2
+
x
1
y
1
)
=
0
⇒
(
x
1
y
2
−
x
1
y
3
)
+
(
x
2
y
3
−
x
2
y
1
)
+
(
x
3
y
1
−
x
3
y
2
)
=
0
⇒
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
=
0
⇒
x
1
(
y
2
−
y
3
)
x
1
x
2
x
3
+
x
2
(
y
3
−
y
1
)
x
1
x
2
x
3
+
x
3
(
y
1
−
y
2
)
x
1
x
2
x
3
=
0
⇒
(
y
2
−
y
3
)
x
2
x
3
+
(
y
3
−
y
1
)
x
1
x
3
+
(
y
1
−
y
2
)
x
1
x
2
=
0
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1
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x
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