Let the point $P\left(\frac{1}{2}, y\right)$ divides the line segment joining the points $A(3,-5)$ and $B(-7,9)$ in the ratio $\mathrm{k}: 1$. Then

$\left(\frac{1}{2}, \mathrm{y}\right)=\left(\frac{\mathrm{k}(-7)+3}{\mathrm{k}+1}, \frac{\mathrm{k}(9)-3}{\mathrm{k}+1}\right)$

$\Rightarrow \frac{-7 \mathrm{k}+3}{\mathrm{k}+1}=\frac{1}{2}$ and $\frac{9 \mathrm{k}-5}{\mathrm{k}+1}=\mathrm{y}$

$\Rightarrow \mathrm{k}+1=-14 \mathrm{k}+6 \Rightarrow \mathrm{k}=\frac{1}{3}$

substituting $k=\frac{1}{3}$ in $\frac{9 k-5}{k+1}=y$, we get

$\frac{\frac{9}{3}-5}{\frac{1}{3}+1}=y \Rightarrow y=\frac{9-15}{1+3}=-\frac{3}{2}$

Therefore, required ratio is $1: 3$ and $\mathrm{y}=-\frac{3}{2}$