The given points are A(-3,2) and B(6,1).
To find x-coordinate we use the following formula
[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1[/tex]
Where a=2, and b=1. Replacing the coordinates, we have
[tex]\begin{gathered} x=\frac{2}{2+1}(6-(-3))+(-3)=\frac{2}{3}(6+3)-3=\frac{2}{3}(9)-3 \\ x=\frac{18}{3}-3=6-3=3 \end{gathered}[/tex]
Then, we find y-coordinate.
[tex]\begin{gathered} y=\frac{a}{a+b}(y_2-y_1)+y_1 \\ y=\frac{2}{2+1}(1-2)+2=\frac{2}{3}(-1)+2=-\frac{2}{3}+2 \\ y=-\frac{2+6}{3}=-\frac{8}{3}=-2.66666\ldots \end{gathered}[/tex]
Therefore, the coordinates are (3, -8/3).
