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Byju's Answer
Standard VI
Mathematics
Collinear Points
Prove that ...
Question
Prove that
A
(
1
,
1
)
,
B
(
2
,
2
)
and
C
(
3
,
3
)
are collinear.
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Solution
W
e
h
a
v
e
t
h
e
g
i
v
e
p
o
i
n
t
s
a
r
e
(
1
,
1
)
(
2
,
2
)
(
3
,
3
)
N
o
w
,
A
r
e
a
o
f
Δ
=
1
2
[
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
]
=
1
2
[
1
(
2
−
3
)
+
2
(
3
−
1
)
+
3
(
1
−
2
)
]
=
1
2
[
1
(
−
1
)
+
2
(
2
)
+
3
(
−
1
)
]
=
1
2
[
−
1
+
4
−
3
]
=
1
2
[
4
−
4
]
=
0
H
e
n
c
e
,
t
h
e
a
r
e
a
o
f
t
r
i
a
n
g
l
e
a
r
e
0
s
o
,
t
h
e
g
i
e
n
p
o
i
t
s
a
r
e
c
o
l
i
n
e
a
r
.
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Similar questions
Q.
Find the equation of the circle which passes through the points
A
(
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,
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and
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,
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)
and whose radius is
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. Show that there are two such circles.
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&
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,
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,
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