Question

given the points a (-1,2) and (7,14), find the coordinates of the point p on directed line segment ab that partitions ab in the ratio 1:3.

Answer 1

Check the picture below.

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ a(-1,2)\qquad b(7,14)\qquad \qquad 1:3 \\\\\\ \cfrac{aP}{Pb} = \cfrac{1}{3}\implies \cfrac{a}{b} = \cfrac{1}{3}\implies 3a=1b\implies 3(-1,2)=1(7,14) \\\\ -------------------------------\\\\ { P=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}$

$\bf -------------------------------\\\\ P=\left(\cfrac{(3\cdot -1)+(1\cdot 7)}{1+3}\quad ,\quad \cfrac{(3\cdot 2)+(1\cdot 14)}{1+3}\right) \\\\\\ P=\left( \cfrac{-3+7}{4}~,~\cfrac{6+14}{4} \right)$