Answer:
B(-3, 1)
Step-by-step explanation:
Let's calculate the distance between the corresponding coordinates of points A and C.
[tex]A(1,\ -5),\ C(-5,\ 4)\\\\|AC|_x=|-5-1|=|-6|=6\\\\|AC|_y=|4-(-5)|=|4+5|=|9|=9[/tex]
We find such B that
[tex]|AB|=\dfrac{2}{3}|AC|=\dfrac{2|AC|}{3}[/tex]
Calculate the unit of division
[tex]a_x=\dfrac{6}{3}=2\\\\b_y=\dfrac{9}{3}=3[/tex]
Therefore the coordinateso f the point B are:
[tex]B(x+2,\ y-3)\\\\x+2=-5+2=-3\\\\y-3=4-3=1\\\\\boxed{B(-3,\ 1)}[/tex]
