Question
A(a,b), B(c,d) and C(e,f) are the vertices of a triangle.
i) AB + BC > AC
ii) Area of the triangle = (12)[a(c-e)+c(f-b)+e(b-d)]
Which of the following are true?
Answer: Option A
:
A
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A
Since A, B and C are the vertices of a triangle, it follows that sum of two sides is greater than the third side. So (i) is correct.
And since the area of a triangle with vertices (x1, y1), (x2 , y2 ) and (x3 , y3 ) is
12[ x1(y2 - y3) + x2( y3 - y1) + x3(y1 - y2)]
= 12 [a (d - f) + c (f - b) + e (b - d)] (by putting x1 = a, y1 = b, x2 = c, y2 = d, x3 = e, y3 = f)
Since the above area is not the same as that given in (ii), (ii) is incorrect.
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