Question

A(-4,2), B(-2,1), C(4,-2) are collinear points. Find the ratio in which B divides AC from A.

Answer 1

Solve the above question as given below in the attachment.

Answer 2

Let B divides AC in m : n ratio from A.
use formula ,
$\bf{(x,y)=\{\frac{mx_2+nx_2}{m+n},\frac{my_2+ny_1}{m+n}\}}$

-2 = (m × 4 + n × -4)/(m + n)

=> -2 = (4m - 4n)/(m + n)

=> -2 × (m + n) = (4m - 4n)

=> -2m - 2n = 4m - 4n

=> -2m - 4m = 2n - 4n

=> -6m = -2n

hence, m/n = 1 : 3