Answer:
The answer to your question is: y = -54 / 11
Step-by-step explanation:
Data
A (3, 0)
B (12, -9)
r = 6/5
Formula
y = [tex]\frac{y1 + ry2}{1 +r}[/tex]
y = [tex]\frac{0 + (6/5)(-9)}{1 + 6/5}[/tex]
y = [tex]\frac{-54/ 5}{11/5}[/tex]
y = -54/11
[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ A(3,0)\qquad B(12,-9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{6:5} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{6}{5}\implies \cfrac{A}{B} = \cfrac{6}{5}\implies 5A=6B\implies 5(3,0)=6(12,-9)\\\\[-0.35em] ~\dotfill\\\\ C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf C=\left(\cfrac{(5\cdot 3)+(6\cdot 12)}{6+5}\quad ,\quad \cfrac{(5\cdot 0)+(6\cdot -9)}{6+5}\right) \\\\\\ C=\left( \cfrac{15+72}{11}~~,~~\cfrac{0-54}{11} \right)\implies C\left(\qquad \qquad ~~,~~-\cfrac{54}{11} \right)[/tex]
