CEMC Banner

Problem of the Week
Problem D
Can You C It?

The line with equation \(y = -\frac{3}{4}x + 18\) crosses the positive \(x\)-axis at point \(B\) and the positive \(y\)-axis at point \(A\). The origin, \(O\), and points \(A\) and \(B\) form the vertices of a triangle.

Point \(C(r,s)\) lies on the line segment \(AB\) such that the area of \(\triangle AOB\) is three times the area of \(\triangle COB\).

Determine the values of \(r\) and \(s\).