Question

What is the point that will cut the segment A(-5,-3) and B(10,9) into the ratio 1:2?

Answer 1

let's say the point is C, cutting AB to a 1:2 ratio from A to B.

`\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-5,-3)\qquad B(10,9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-5,-3)=1(10,9)\\\\[-0.35em] ~\dotfill\\\\ C=\left(\frac{\textit{sum of`

`\bf C=\left(\cfrac{(2\cdot -5)+(1\cdot 10)}{1+2}\quad ,\quad \cfrac{(2\cdot -3)+(1\cdot 9)}{1+2}\right) \\\\\\ C=\left( \cfrac{-10+10}{3}~~,~~\cfrac{-6+9}{3} \right)\implies C=\left( \cfrac{0}{3}~,~\cfrac{3}{3} \right)\implies C=(0,1)`