ANSWER
[tex]( - \frac{23}{5} , - 4)[/tex]
EXPLANATION
Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by
[tex]x = \frac{ mx_2+nx_1}{m + n} [/tex]
[tex]y= \frac{ my_2+ny_1}{m + n} [/tex]
Where m=3 and n=2
[tex]x = \frac{ 3 ( - 9)+2(2)}{3+ 2} [/tex]
[tex]x = \frac{ - 23}{5} [/tex]
[tex]y= \frac{ 3( - 6)+2( - 1)}{3 + 2} [/tex]
[tex]y= \frac{ - 20}{5} = - 4[/tex]
The point is
[tex]( - \frac{23}{5} , - 4)[/tex]
