The segment joining A(-3, 10) and B(6, -8) is divided by a point P in the ratio k : 1.
If the $y$-coordinate of P is -2, find k and the $x$-coordinate of P.

$\frac{-8k+10}{k+1}=-2$ gives $-8k+10=-2k-2$, so $12=6k$ and $k=2$. Then $x=\frac{2\cdot 6+1\cdot (-3)}{3}=\frac{9}{3}=3$. The option $k=0.5$ writes the ratio as 1 : $k$, inverted, and consistently produces $x=0$; $k=1$ is the midpoint case, whose $y$-coordinate is 1, not -2; the option $k=2,x=0$ has the right $k$ but computes $x$ as $k{x}_1+x_2$, i.e. with m and n swapped.