Answer: (-4.5,-3)
Step-by-step explanation:
(-9,-2) (9,-6) 1:3
[tex]\displaystyle\\\boxed {x=\frac{x_1+\lambda x_2}{1+ \lambda} \ \ \ \ \ \ y=\frac{y_1+\lambda y_2}{1+\lambda} }[/tex]
[tex]\displaystyle\\x_1=-9\ \ \ \ x_2=9\ \ \ \ \ y_1=-2\ \ \ \ \ \ y_2=-6\ \ \ \ \ \lambda=1:3=\frac{1}{3} \\\\x=\frac{-9+(\frac{1}{3})(9) }{1+\frac{1}{3} } \\\\x=\frac{-9+3}{\frac{(1)(3)+1}{3} } \\\\x=\frac{-6}{\frac{3+1}{3} } \\\\x=\frac{(-6)(3)}{4} \\\\x=\frac{-18}{4}\\\\x=-4.5 \\\\y=\frac{-2+(\frac{1}{3} )(-6)}{1+\frac{1}{3} } \\\\y=\frac{-2+(-2)}{\frac{4}{3} } \\\\y=\frac{(-4)(3)}{4} \\\\y=-3\\Thus,(-4.5,-3)[/tex]
