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

Question

asked Apr 25, 2021 79.9k views

1 Answer

Pankaj Singh · Answer 1 · 2021-05-02T02:10:19+0000

Answer:

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|=(2)/(3)|AC|=(2|AC|)/(3)

Calculate the unit of division

$a_x=(6)/(3)=2\\\\b_y=(9)/(3)=3$

Therefore the coordinateso f the point B are:

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