1. Tardigrade
  2. Question
  3. Mathematics
  4. Let the area of the triangle with vertices A (1, α), B (α, 0) and C (0, α) be 4 sq. units. If the point (α,-α),(-α, α) and (α2, β) are collinear, then β is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let the area of the triangle with vertices $A (1, \alpha)$, $B (\alpha, 0)$ and $C (0, \alpha)$ be $4$ sq. units. If the point $(\alpha,-\alpha),(-\alpha, \alpha)$ and $\left(\alpha^{2}, \beta\right)$ are collinear, then $\beta$ is equal to

JEE MainJEE Main 2022Straight Lines

Solution:

$\frac{1}{2}\begin{vmatrix}\alpha & 0 & 1 \\ 1 & \alpha & 1 \\ 0 & \alpha & 1\end{vmatrix}=\pm 4$
$\alpha=\pm 8$
Now given points $(8,-8),(-8,8),(64, \beta)$
OR $(8,8),(8,8),(64, \beta)$
are collinear $\Rightarrow$ Slope $=-1$.
$\beta=-64$