Find the equations of the asymptotes of the hyperbola $\frac{{(x-1)}^2}{16}-\frac{{(y+2)}^2}{9}=1$.

$y-2=\pm \frac{4}{3}(x+1)$

$y+2=\pm \frac{4}{3}(x-1)$

$y-1=\pm \frac{3}{4}(x+2)$

$y+2=\pm \frac{3}{4}(x-1)$