find the area of triangle whose vertices are as follows (a,b) (b,c) (c,a)
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Answer:
Correct option is A)
Area of a triangle (A)=
∣
∣
∣
∣
∣
∣
2
x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)
∣
∣
∣
∣
∣
∣
Hence, substituting the points (x
1
,y
1
)=(a,b+c) , (x
2
,y
2
)=(a,b−c) and (x
3
,y
3
)=(−a,c)
A=
∣
∣
∣
∣
∣
∣
2
a(b−c−c)+a(c−b−c)−a(b+c−b+c)
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
2
a(b−2c)+a(−b)−a(2c)
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
2
ab−2ac−ab−2ac
∣
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
∣
2
−4ac
∣
∣
∣
∣
∣
∣
=2ac square units
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