Solution:

$P_{00}(0,0,1), P_{01}(1,1,1), P_{10}(1,0,0)$ and $P_{11}(0,1,0)$

Equation of bilinear surface is given by,

$P(u, v)=(1-u)(1-v) P_{00}+u(1-v) P_{10}+(1-u) v P_{01}+u v P_{11}$

The values for x, y and z coordinates can be determined as,

$\begin{aligned} P_{x}(u, v) &=(1-u)(1-v)(0)+u(1-v)(1)+(1-u) v(1)+u v(0) \\ &=u+v-2 u v \\ P_{y}(u, v) &=(1-u)(1-v)(0)+u(1-v)(0)+(1-u) v(1)+u v(1) \\ &=v \\ P_{z}(u, v) &=(1-u)(1-v)(1)+u(1-v)(0)+(1-u) v(1)+u v(0) \\ &=1-u \end{aligned}$

$\therefore P(u, v)=[u+v-2 u v \quad v \quad 1-u]$

At $u=0.5 \ and \ v=0.5,$ coordinate of point is

$P(u, v)=\left[\begin{array}{ccc}{0.5} & {0.5} & {0.5}\end{array}\right]$