Question

Find the coordinates of point p that partition AB in the ratio 2:3 where A (-8,13) and B (2,-2)

Answer 1

Check the picture below.

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(-8,13)\qquad B(2,-2)\qquad \qquad 2:3\textit{ from A to B} \\\\\\ \cfrac{AP}{PB} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-8,13)=2(2,-2)\\\\ -------------------------------\\\\ { P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------$

$\bf P=\left(\cfrac{(3\cdot -8)+(2\cdot 2)}{2+3}\quad ,\quad \cfrac{(3\cdot 13)+(2\cdot -2)}{2+3}\right) \\\\\\ P=\left(\cfrac{-24+4}{5}~,~\cfrac{39-2}{5} \right)$