Question

If the points $(3,k)$ and $(2,-6)$ lies on opposite sides of a line $3x-4y=k$, where $k\in R$, then $k$ belongs to the interval

Answer 1

If points are$(x1,y1),(x2,y2)$

If points are on opposite sides then $ax1+by1+c$ and $ax2+by2+c$ have opposite signs

therefore case 1 :- $9-5k>0$ and $30-k<0$

this is not possible

Case2: $9-5k<0,30-k>0$

$\frac{9}{5}<k<30$