In the standard \((x,y)\) coordinate plane below, a shaded square is shown with vertices at \((2,3)\), \((2,4)\), \((3,3)\), and \((3,4)\). Two lines, \(y=rx\) and \(y=sx\), each intersect the shaded square at exactly 1 point. Given that \(r\neq s\), what is the positive difference of \(r\) and \(s\) ?

Summary Submit Skip Question

A line starting at the origin can intersect at 1 point only if it goes through \((2,4)\) or \((3,3)\).

The corresponding slopes of these two lines would be \(\dfrac{4}{2}\) and \(\dfrac{3}{3}\).

$$ \frac{4}{2} - \frac{3}{3} $$ $$ 2- 1 = \boxed{1} $$