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Byju's Answer
Standard X
Mathematics
Area of a Triangle Given Its Vertices
Check whether...
Question
Check whether
(
5
,
−
2
)
,
(
6
,
4
)
and
(
7
,
−
2
)
are the vertices of an isosceles triangles.
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Solution
Let ABC be the triangle
A
(
5
,
−
2
)
,
B
(
6
,
4
)
,
C
(
7
,
−
2
)
By distance formula
A
B
=
√
(
5
−
6
)
2
+
(
−
2
−
4
)
2
=
√
(
−
1
)
2
+
(
−
6
)
2
√
37
B
C
=
√
(
6
−
7
)
2
+
(
4
−
(
−
2
)
2
=
√
(
−
1
)
2
+
(
6
)
2
=
√
37
C
A
=
√
(
7
−
5
)
2
+
(
−
2
−
(
−
2
)
)
2
=
√
(
2
)
2
+
0
=
2
Since
A
B
=
B
C
=
√
37
Hence
(
5
,
−
2
)
,
(
6
,
4
)
&
(
7
,
−
2
)
are vertices of isosceles triangle.
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Q.
Check whether (5, − 2), (6, 4) and (7, − 2) are the vertices of an isosceles triangle.