Answer:
[tex]A(0.8,\ 1.4)\ \text{or }\ A\left(\dfrac{4}{5},\dfrac{7}{5}\right)[/tex]
Step-by-step explanation:
If point [tex]A(x,y)[/tex] divides the segment with endpoints [tex]C(x_1,y_1)[/tex] and [tex]D(x_2,y_2)[/tex] in the ratio [tex]m:n,[/tex]
then
[tex]x=\dfrac{nx_1+mx_2}{m+n}\\ \\y=\dfrac{ny_1+my_2}{m+n}[/tex]
In your case,
[tex]C(-4,3)\\ \\D(8,-1)\\ \\m:n=2:3[/tex]
then
[tex]x=\dfrac{3\cdot (-4)+2\cdot 8}{2+3}=\dfrac{-12+16}{5}=\dfrac{4}{5}=0.8\\ \\y=\dfrac{3\cdot 3+2\cdot (-1)}{2+3}=\dfrac{9-2}{5}=\dfrac{7}{5}=1.4[/tex]
Thus,
[tex]A(0.8,\ 1.4)\ \text{or }\ A\left(\dfrac{4}{5},\dfrac{7}{5}\right)[/tex]
