Question

If the point C(k, 4) divides the join of the points A(2, 6) and B(5, 1) in the ratio 2 : 3 then the value of k is [CBSE 2013C]
(a) 16 (b) $\frac{28}{5}$ (c) $\frac{16}{5}$ (d) $\frac{8}{5}$

Answer 1

The point C(k, 4) divides the join of the points 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, the correct answer is option (c).