Question

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

Answer 1

B(-3, 1)

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)}`