Given A , B and C are collinear
AB : AC = 2/5
A = ( -3 , 6 )
B = ( n , q )
C = ( -3 , -4 )
Note : the x coordinates of A = x-coordinates of C = -3
As the three points are collinear
So, the x-coordinates of the point B = -3
so, n = -3
Now, we will find the y-coordinates of the point B
AB : AC = 2/5
So,
[tex]\begin{gathered} \frac{ya-yb}{ya-yc}=\frac{2}{5} \\ \frac{6-q}{6-(-4)}=\frac{2}{5} \\ \frac{6-q}{10}=\frac{2}{5} \\ 5(6-q)=20 \\ 6-q=4 \\ q=6-4 \\ q=2 \end{gathered}[/tex]so, the y-coordinates of the point B = q = 2
so, n = -3 and q = 2
The ordered pair of B is ( -3 , 2 )
