If the point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3 then find the value of k.

Here, the point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3. So

$k=\frac{2 \times 5+3 \times 2}{2+3}$

$=\frac{10+6}{5}$

$=\frac{16}{5}$

Hence, $k=\frac{16}{5}$.