Question

In each of the following find the value of $k$, for which the points are collinear..
(ii) $(8,1),(k,-4),(2,-5)$

Answer 1

Let the points are

$A\left(8,1\right)B\left(K,-4\right)C\left(2,-5\right)$

For collinearity

$Areaof\Delta ABC$

$\frac{1}{2}\left|8\left(-4+5\right)+K\left(-5-1\right)+2\left(1+4\right)\right|=0$

$\left|8-6k+10\right|=0$

$18-6k=0$

$6k=18$

$k=3$