if point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1 then p must have coordinates of?

That means P is the midpoint:

[tex]P=\left(\frac{x_1+x_2}{2}\;,\; \frac{y_1+y_2}{2} \right) \\ \\ P=\left(\frac{-5+1}{2}\;,\; \frac{11+5}{2} \right)=\left(\frac{-4}{2}\;,\; \frac{16}{2} \right) \\ \\ P=(-2\;,\;8)[/tex]