Question

Question 3 (10 points)

Answer 1

now this assuming that M partitions XY on a 4:1 ratio "from X to Y", Check the picture below.

$\textit{internal division of a line segment using ratios} \\\\\\ X(1,-2)\qquad Y(10,3)\qquad \qquad \stackrel{\textit{ratio from X to Y}}{4:1} \\\\\\ \cfrac{X\underline{M}}{\underline{M} Y} = \cfrac{4}{1}\implies \cfrac{X}{Y} = \cfrac{4}{1}\implies 1X=4Y\implies 1(1,-2)=4(10,3)$

$(\stackrel{x}{1}~~,~~ \stackrel{y}{-2})=(\stackrel{x}{40}~~,~~ \stackrel{y}{12})\implies M=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{1+40}}{4+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-2+12}}{4+1} \right)} \\\\\\ M=\left( \cfrac{41}{5}~~,~~ \cfrac{10}{5}\right)\implies M=\left(8\frac{1}{5}~~,~~2 \right)$