Answer: C(-1,0)
Step-by-step explanation:
A(-3,-1) B(7,4) AC:CB=1:4
[tex]If\ you\ know\ two\ points\ of\ the\ plane\ A(x_A,y_A),\ B(x_B,y_B) \ then\ the\[/tex]
[tex]coordinates \ of \ the\ point\ C(x_C,y_C),\ which\ divides\ the \ segment \ in\ the\ relation[/tex]
[tex]\lambda=\frac{AC}{CB}\ are\ expressed \ by\ the\ formulas:[/tex]
[tex]\boxed {x_C=\frac{x_A+\lambda x_B}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \ \ \boxed {y_C=\frac{y_A+\lambda y_B}{1+\lambda} }[/tex]
Hence,
[tex]\displaystyle\\\lambda=\frac{AC}{CB}=\frac{1}{4} =0.25[/tex]
[tex]\displaystyle\\x_C=\frac{-3+0.25*7}{1+0.25 }\\\\x_C=\frac{-3+1.75}{1.25} \\\\x_C=\frac{-1,25}{1.25} \\\\x_C=-1[/tex]
[tex]\displaystyle\\y_C=\frac{-1+0.25*4}{1+0.25} \\\\y_C=\frac{-1+1}{1.25}\\\\y_C=\frac{0}{1.25}\\\\y_C=0[/tex]
Thus, C(-1,0)
