Points P, Q and R have coordinates $(1, 1)$, $(5, 11)$ and $(9, 1)$ respectively. M is the midpoint of QR.

1. Apply the midpoint formula to points Q and R.

For $Q(5,11)$ and $R(9,1)$,
$M=\left(\frac{5+9}{2},\frac{11+1}{2}\right)=\left(\frac{14}{2},\frac{12}{2}\right)=(7,6).$

1. Calculate the gradient of $PM$ using the coordinates of $P$ and $M$.

For $P(1,1)$ and $M(7,6)$,

$\text{gradient of } PM=\frac{6-1}{7-1}=\frac{5}{6}.$

1. Find the lengths of the two sides forming angle $QPR$.

$PQ=\sqrt{(5-1)^2+(11-1)^2}=\sqrt{4^2+10^2}=\sqrt{116}$
$PR=\sqrt{(9-1)^2+(1-1)^2}=\sqrt{8^2+0^2}=8$

2. Decide whether $PM$ can be the angle bisector of $\angle QPR$.

Since $PQ=\sqrt{116}\ne 8=PR$, triangle $PQR$ is not isosceles with $PQ=PR$.

So the median $PM$ to $QR$ does not bisect $\angle QPR$.