Question

Find the coordinate of point P that lies along the directed line segment from A (3, 4) to B (6, 10) and partitions the segment in the ratio of 3:2.
Type the coordinate in the decimal form

Answer 1

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(3,4)\qquad B(6,10)\qquad \qquad 3:2 \\\\\\ \cfrac{AP}{PB} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(3,4)=3(6,10)\\\\ -------------------------------\\\\ { P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------$

$\bf P=\left(\cfrac{(2\cdot 3)+(3\cdot 6)}{3+2}\quad ,\quad \cfrac{(2\cdot 4)+(3\cdot 10)}{3+2}\right) \\\\\\ P=\left( \cfrac{6+18}{5}~~,~~\cfrac{8+30}{5} \right)\implies \left( \cfrac{24}{5}~~,~~\cfrac{38}{5} \right)\implies \left( 4\frac{4}{5}~~,~~7\frac{3}{5} \right)$