Over or Under Determined?

Geometry Level 4

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 \(U\).

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