The point C divides the line AB in ratio 3:2 means that,
Determine the coordinate of point B.
[tex]\begin{gathered} (3.6,-0.4)=(\frac{3x-2\cdot6}{3+2},\frac{3y+2\cdot5}{5}) \\ (3.6,-0.4)=(\frac{3x-12}{5},\frac{3y+10}{5}) \end{gathered}[/tex]
Simplify the equation for x and y.
[tex]\begin{gathered} \frac{3x-12}{5}=3.6 \\ 3x-12=3.6\cdot5 \\ 3x=18+12 \\ x=\frac{30}{3} \\ =10 \end{gathered}[/tex]
For y,
[tex]\begin{gathered} -0.4=\frac{3y+10}{5} \\ 3y+10=-0.4\cdot5 \\ 3y=-2-10 \\ y=-\frac{12}{3} \\ =-4 \end{gathered}[/tex]
So coordinates of the point B are (10,-4).
Determine the coordinates of the point D which divide the line CB in 4:5 ratio.
[tex]\begin{gathered} D(x,y)=(\frac{4\cdot10+5\cdot3.6}{4+5},\frac{4\cdot(-4)+5\cdot(-0.4)}{4+5}) \\ =(\frac{40+18}{9},\frac{-16-2}{9}) \\ =(\frac{58}{9},-2) \end{gathered}[/tex]
So coordinates of point D is (58/9,-2).
