Joseph was asked the following question, ``If \(\overline{LM} \) is partitioned in the ratio 5:4 by the point A, and L is (1, 6) and M is (8, -3), what is the coordinate of A?'' His work is shown below. Find his mistake and find the correct answer.

\(\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)\)

\(\left(\frac{5(1)+4(8)}{5+4},\frac{5(6)+4(-3)}{5+4}\right)\)

\(\left(\frac{37}{9},\frac{18}{9}\right)\)

\(\left(\frac{37}{9},\ 2\right)\)