Question

Point B is collinear with A and C and partitions AC in a 3:4 ratio. B is located at (4,1) and C is located at (12,5). Find the coordinates of endpoint A. Show steps

Answer 1

`A(-(20)/(3) ,-(13)/(3))`

Explanation:

Point B partitions AC in a 3:4 ratio.

B is located at (4,1) and C is located at (12,5).

Let
`(x_1,y_1)` be the coordinates of A.

Then
`((mx_1+nx_2)/(m+n), (my_1+ny_2)/(m+n))=(4,1)`

But m:n=3:4 implies m=3 and n=4 and
`(x_2=12,y_2=5)`

`((3x_1+4*12)/(3+4), (3y_1+4*5)/(3+4))=(4,1)`

`((3x_1+48)/(7), (3y_1+20)/(7))=(4,1)`

`(3x_1+48)/(7)=4, (3y_1+20)/(7)=1`

`3x_1+48=28, 3y_1+20=7`

`3x_1=-20, 3y_1=-13`

`x_1=-(20)/(3) , y_1=-(13)/(3)`