Question

Need help with the second part, I can plot but what seems to be a ratio I'm drawing a major blank

Answer 1

I would suggest labeling the quadrants, plotting the points, labeling the points, and if you don't understand after that, I'm sorry but this is all I can help I hope it proved useful in some way.

Answer 2

Check the picture below, notice the ratios, from AP to PB

$\bf \textit{internal division of a line segment} \\ \quad \\ A(-6,-5)\qquad B(4,0)\qquad ratio1=2\qquad ratio2=3\qquad 2:3\\ \quad \\ \quad \\ \cfrac{A{ P }}{{ P }B}=\cfrac{ratio1}{ratio2}\implies \cfrac{A{ }}{{ }B}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot A=ratio1\cdot B\quad \\\\\\ 3(-6,-5)=2(4,0) \\ \quad \\ {{ P=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}\\ \quad$

$\bf \qquad thus\qquad \\ \quad \\ P=\left(\cfrac{(3\cdot -6)+(2\cdot 4)}{2+3}\quad ,\quad \cfrac{(3\cdot -5)+(2\cdot 0)}{2+3}\right)$