bearing in mind that, the ratio here is 1:7 form A to B, that matters, because, the AB segment gets split in 8 pieces, and AP takes 1 slice whilst PB takes 7 slices
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(-8,-3)\qquad B(6,12)\qquad
ratio1=1\qquad ratio2=7\qquad 1:7
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\cfrac{AP}{PB} = \cfrac{1}{7}\implies \cfrac{A}{B} = \cfrac{1}{7}\implies 7\cdot A=1\cdot B
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7(-8,-3)=1(6,12)\\\\
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[tex]\bf { P=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}\\\\
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P=\left(\cfrac{(7\cdot -8)+(1\cdot 6)}{1+7}\quad ,\quad \cfrac{(7\cdot -3)+(1\cdot 12)}{1+7}\right)[/tex]
