Question

If the vertices of a triangle are (1, a), (2, b) and $(c^2,-3)$ then, the condition for which the centroid lies on x-axis, is

• A. ab = 0
• B. a + b = 3
• C. a - b = 3
• D. a - b = 0

Answer 1

The correct option is B a + b = 3

Let G(x, 0) be the centroid of $\Delta ABC$ whose vertices are A(1, a), B(2, b) and $C(c^2,-3)$.



for centroid G,

$x=\frac{1+2+c^2}{3}=\frac{3+c^2}{3}$

$O=\frac{a+b+(-3)}{3}\Rightarrow O=a+b-3$

$\Rightarrow 3=a+b$

$\therefore a+b=3$

So, option (b) is correct.