Question

Find the coordinates of point B on line AC such that AB is 2/3 of AC

Answer 1

Answer:

B(-3, 1)

Step-by-step explanation:

Let's calculate the distance between the corresponding coordinates of points A and C.

$A(1,\ -5),\ C(-5,\ 4)\\\\|AC|_x=|-5-1|=|-6|=6\\\\|AC|_y=|4-(-5)|=|4+5|=|9|=9$

We find such B that

$|AB|=\dfrac{2}{3}|AC|=\dfrac{2|AC|}{3}$

Calculate the unit of division

$a_x=\dfrac{6}{3}=2\\\\b_y=\dfrac{9}{3}=3$

Therefore the coordinateso f the point B are:

$B(x+2,\ y-3)\\\\x+2=-5+2=-3\\\\y-3=4-3=1\\\\\boxed{B(-3,\ 1)}$