Question

Find the coordinates of point p which divides the line segment from A=(0,4)to B=(6,8)in a ratio of 1:2

Answer 1

check the picture below.


`\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(0,4)\qquad B(6,8)\qquad \qquad 1:2\quad \textit{ from A to B} \\\\\\ \cfrac{AP}{PB} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(0,4)=1(6,8) \\\\ -------------------------------\\\\ { P=\left(\cfrac{\textit{sum of`


`\bf P=\left(\cfrac{(2\cdot 0)+(1\cdot 6)}{1+2}\quad ,\quad \cfrac{(2\cdot 4)+(1\cdot 8)}{1+2}\right) \\\\\\ P=\left( \cfrac{0+6}{3}~,~\cfrac{8+8}{3} \right)`