Hello, Punch!
Was that the original wording of the problem?
It's written very badly.
Given points $\displaystyle B\left(\tfrac{1}{2},\:3\right)$ and $\displaystyle E(1,\:1)$
Find the coordinates of point D so that $\displaystyle BE : ED = 1:3$ Here's a back-door approach . . .
Code:
½
B(½,3)o - +
\ :
d \ : 2
\:
E(1,1)o - - - +
\ :
\ :
\ :
3d \ :
\ :
\ :
\:
D o
Going from $\displaystyle B$ to $\displaystyle E$, we moved $\displaystyle \tfrac{1}{2}$ unit right and 2 units down.
. . And we moved a diagonal distance $\displaystyle d.$
Going from $\displaystyle E$ to $\displaystyle D$, we want to move a diagonal distance $\displaystyle 3d.$
. . Hence, we must triple our previous moves.
From $\displaystyle E$, we move $\displaystyle {\color{blue}\tfrac{3}{2}}$ units right and 6 units down.
Therefore, point $\displaystyle D$ is: .$\displaystyle \left(\tfrac{5}{2},\;\text{-}5\right)$