Question

find the coordinates of the point p that divides the direct line segment from A to B in the given ratio A ( -9,5) B (15,-11)7 to 1

Answer 1

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-9,5)\qquad B(15,-11)\qquad \qquad \stackrel{\textit{ratio from A to B}}{7:1} \\\\\\ \cfrac{A\underline{p}}{\underline{p} B} = \cfrac{7}{1}\implies \cfrac{A}{B} = \cfrac{7}{1}\implies 1A=7B\implies 1(-9,5)=7(15,-11)\\\\ -------------------------------$

$\bf p=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\ -------------------------------\\\\ p=\left(\cfrac{(1\cdot -9)+(7\cdot 15)}{7+1}\quad ,\quad \cfrac{(1\cdot 5)+(7\cdot -11)}{7+1}\right) \\\\\\ p=\left(\cfrac{-9+105}{8}~~,~~\cfrac{5-77}{8} \right)\implies p=\left( \cfrac{96}{8}~~,~~\cfrac{-72}{8} \right) \\\\\\ p=(12~,~-9)$