Correct Answer - Option 4 : 0
Concept:
Area of the triangle if there vertices are (x1,y1), (x2,y2), (x3,y3). Then,
Area = \(\frac{1}{2}\)[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]
Given:
(a, b + c), (b, c + a), (c, a + b) are vertices of triangle.
Calculation:
Area = \(\frac{1}{2}\)[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]
= \(\frac{1}{2}\)[a( c + a - a - b) + b(a + b - b - c) + c(b + c - c - a)]
= \(\frac{1}{2}\)[a(c - b) + b(a - c) + c(b - a)]
= \(\frac{1}{2}\)[ca - ab + ab - bc + bc -ac]
= 0
