The $1^{\mathrm{st}}$ point of trisection of segment joining (3, –1, 2) and (9, 5, 2) is

The given points are $A\left(3,-1,2\right),B\left(9,5,2\right)$

The coordinates of a point which divides the line segment $AB$ in the ratio $1:2$ internally is hte point of trissection of segment 

Hence, 

$\begin{array}{rcl}C& =& \left(\frac{9+6}{3},\frac{5-2}{3},\frac{2+4}{3}\right)\\ & =& \left(5,1,2\right)\end{array}$

Therefore, the first trisecting point of the linesegment joining $A\left(3,-1,2\right),B\left(9,5,2\right)$ is $\boxed{\left(5,1,2\right)}$