If the points (2, -3), (λ, -1) and (0, 4) are collinear, then the val…

The correct answer is Option (4) → $\frac{10}{7}$

Given points are $(2,-3)$, $(\lambda,-1)$ and $(0,4)$.

For collinearity, slope between $(2,-3)$ and $(\lambda,-1)$ equals slope between $(\lambda,-1)$ and $(0,4)$.

$\frac{-1-(-3)}{\lambda-2}=\frac{4-(-1)}{0-\lambda}$

$\frac{2}{\lambda-2}=\frac{5}{-\lambda}$

$2(-\lambda)=5(\lambda-2)$

$-2\lambda=5\lambda-10$

$-7\lambda=-10$

$\lambda=\frac{10}{7}$