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Byju's Answer
Standard X
Mathematics
Distance between Two Points on the Same Coordinate Axes
In each of th...
Question
In each of the following find the value of
k
, for which the points are collinear.
(i)
(
7
,
−
2
)
,
(
5
,
1
)
,
(
3
,
k
)
(ii)
(
8
,
1
)
,
(
k
,
−
4
)
,
(
2
,
−
5
)
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Solution
(i) let the given points are
A
(
7
,
−
2
)
,
B
(
5
,
1
)
and
C
(
3
,
k
)
These point are collinear if area (
△
A
B
C
)=0
⇒
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
=
0
Here
x
1
,
y
1
)
=
(
7.
−
2
)
(
x
2
,
y
2
)
=
(
5
,
1
)
(
x
3
,
y
3
)
=
(
3
,
k
)
⇒
7
(
1
−
k
)
+
5
(
k
+
2
)
+
3
(
−
2
−
1
)
=
0
⇒
7
−
7
k
+
5
k
+
10
−
9
=
0
⇒
8
−
2
k
=
0
⇒
2
k
=
8
⇒
k
=
4
Hence the given points are collinear for
k
=
4
(i) let the given points are
A
(
8
,
1
),
B
(
k
,
−
4
)
and
C
(
2
,
−
5
)
These point are collinear if area (
△
A
B
C
)=0
⇒
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
=
0
Here
x
1
,
y
1
)
=
(
8
,
1
)
(
x
2
,
y
2
)
=
(
k
,
−
4
)
(
x
3
,
y
3
)
=
(
2
,
−
5
)
⇒
8
(
−
4
+
5
)
+
k
(
−
5
−
1
)
+
2
(
1
+
4
)
=
0
⇒
8
−
6
k
+
10
=
0
⇒
−
6
k
=
−
18
⇒
k
=
3
⇒
k
=
4
Hence the given points are collinear for
k
=
3
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6
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Distance between Two Points on the Same Coordinate Axes
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