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Byju's Answer
Standard X
Mathematics
Area of a Triangle Given Its Vertices
Prove that th...
Question
Prove that the area of triangle with vertices
(
t
,
t
−
2
)
,
(
t
+
2
,
t
+
2
)
,
(
t
+
3
,
t
)
is independent of t.
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Solution
Area of Triangle with vertices
A
(
t
,
t
−
2
)
,
B
(
t
+
2
,
t
+
2
)
,
C
(
t
+
3
,
t
)
A
r
e
a
o
f
△
A
B
C
=
∣
∣ ∣ ∣ ∣
∣
t
t
−
2
t
+
2
t
+
2
t
+
3
t
t
t
−
2
∣
∣ ∣ ∣ ∣
∣
=
1
2
|
t
2
+
2
t
−
t
2
+
4
+
t
2
+
2
t
−
t
2
−
5
t
−
6
+
t
2
+
t
−
6
−
t
2
|
=
1
2
|
−
8
|
=
4
(is independent of t)
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