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

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   

(a) 16

(b) $\frac{28}{5}$

(c) $\frac{16}{5}$

(d) $\frac{8}{5}$

 

Solution:

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).

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