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Byju's Answer
Standard X
Mathematics
Collinear Points
Find the rela...
Question
Find the relation between
x
and
y
if the points
A
(
x
,
y
)
,
B
(
−
5
,
7
)
and
C
(
−
4
,
5
)
are collinear.
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Solution
Area of triangle
=
1
2
[
x
1
(
y
2
−
y
1
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
3
)
]
=
1
2
[
x
(
7
−
5
)
+
5
(
5
−
y
)
−
4
(
4
−
7
)
]
Given
A
,
B
and
C
are collinear, then area of triangle must be zero.
∴
1
2
[
x
(
7
−
5
)
+
5
(
5
−
y
)
−
4
(
4
−
7
)
]
=
0
⇒
1
2
[
2
x
−
25
+
5
y
−
4
y
+
25
]
=
0
⇒
1
2
(
2
x
+
y
+
3
)
=
0
Then, relation between
x
and
y
is
2
x
+
y
+
3
=
0
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