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NIMCET 2012 Question Paper with solutions
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© examsnet.com
Question : 16
Total: 120
If (4, - 3) and (- 9, 7) are the two vertices of a triangle and (1, 4) is its centroid, then the area of triangle is
138
2
319
2
183
2
381
2
Validate
Solution:
We know that,
Centroid of the triangle,
G =
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
= (1 , 4)
⇒
{
4
−
9
+
x
3
,
−
3
+
7
+
y
3
}
= (1 , 4)
⇒
(
x
−
5
3
,
y
+
4
3
)
= (1 , 4)
⇒ x - 5 = 3 ⇒ x = 8
and y + 4 = 12 ⇒ y = 8
So, third vertex of a Δ ABC is (8, 8).
Now, area of Δ ABC =
1
2
|
4
−
3
1
−
9
7
1
8
8
1
|
Use
R
2
→
R
2
−
R
1
,
R
3
→
R
3
−
R
1
=
1
2
|
4
−
3
1
−
13
10
0
4
11
0
|
Expand with respect to
C
3
=
1
3
|(- 143 - 40)| =
1
2
|- 183| =
183
2
© examsnet.com
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