Find the coordinates of B.

[Jerome2013]

The point P(-5,-6) divides the line joining A(7,6) and B(x,y) in the ratio 1:3.

 

[pka]

The point P(-5,-6) divides the line joining A(7,6) and B(x,y) in the ratio 1:3.

I will tell you how to do this. But keeping in line with forum policy will not do it.

The line segment \(\displaystyle \overline{AB}=<t(x-7)+7,~t(y-6)+6>,~0\le t\le 1~.\)

Note that \(\displaystyle A\) corresponds to \(\displaystyle t=0\) and \(\displaystyle B\) corresponds to \(\displaystyle t=1\).

So \(\displaystyle P\) corresponds to \(\displaystyle t=\frac{1}{4}\). Now you can find \(\displaystyle (x,y)\).