Question

CD has the endpoints C(3, 2) and D(–5, –2). Charlie wants to place the point E at the point that partitions this line segment in a 3:1 ratio. What are the coordinates of the point E?

Answer 1

(-3,-1 ), got it right on e2020

Answer 2

So ... notice the picture below... the ratio is 3:1 from C to D, meaning the segment CE takes 3 units, whilst the ED segment takes 1

anyhow

$\bf \textit{internal division of a line segment} \\ \quad \\\\ C(3,2)\qquad D(-5,-2)\qquad ratio1=3\qquad ratio2=1\qquad 3:1 \\\\\\ \cfrac{C\underline{ E }}{\underline{ E }D}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot C=ratio1\cdot D \\\\\\ 1(3,2)=3(-5,-2) \\ \quad \\\\ {{ E=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}$

$\bf \qquad thus \\\\\\ E=\left(\cfrac{(1\cdot 3)+(3\cdot -5)}{3+1}\quad ,\quad \cfrac{(1\cdot 2)+(3\cdot -2)}{3+1}\right)$