A civil engineer at the World Bank is designing a sustainable pedestrian bridge that follows a linear path defined by the parametric equation \(\mathbfr(t) = eginpmatrix 1 \ -2 \endpmatrix + t eginpmatrix 3 \ 1 \endpmatrix\). They need to locate the point on this line closest to a proposed water source located at \(eginpmatrix 5 \ 4 \endpmatrix\). Find the coordinates of this closest point.