Over or Under Determined?

If $\overline{US}=5$ and $\overline{UR}=4$ , find $|R|$

Details and assumptions:

$|R|$ means the magnitude of point $R$ from the origin.

(You really don't need to read everything below, it's simply a clarification of the diagram above).

Note: ignore points C and D on the diagram, they're incorrectly labeled.

Two different parallel lines $A$ and $B$ are drawn with the same slope $m$ such that $m$ is a positive integer, line $A$ intersects the origin, and line $A$ intersects the y-axis above line $B$ .

A third line $C$ is drawn with slope $n$ such that $0<n<m$ , it intersects line $B$ at point $S$ with coordinates $(j,k)$ , and it also intersects the origin.

K, at this point you should probably just look at the diagram, but feel free to keep reading.

A forth line $D$ is drawn with slope $p$ such that $p<0$ , it intersects line $A$ at point $T$ with coordinates $(g,h)$ such that $g<j$ and $h<k$ , it intersects line $C$ at point $R$ , and it has the same x intercept as line $B$ .

A fifth line $E$ is drawn parallel to the x-axis such that point $T$ lies on this line and line $E$ intersects line $C$ at point $U$ .