Question

If the vertices of a triangle are $(1,a)(2,b)$ and $(c^2,-3)$. Then,
l. The centroid cannot lie on the Y-axis.
II. The condition that the centroid may lie on the X- axis is a + b = 3

• A. Both I and II are true
• B. Only I is true
• C. Only II is true
• D. Both I and II are false

Answer 1

Answer: (A)

Both I and II are true

$\begin{array}{c}Centroid=\left(\frac{1+2+c^2}{3},\frac{a+b-3}{3}\right)\\ =\left(\frac{3+c^2}{3},\frac{a+b-3}{3}\right)\\ Ifa+b=3\\ thencentroid=\left(\frac{3+c^2}{3},0\right)\\ Hence,optionAiscorrectanswer.\end{array}$