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 ______.

Options

• 16

• `28/5`

• `16/5`

• `8/5`

Answer 1

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 `underlinebb(16/5)`.

Explanation:

If C divides AB in the ratio AC : CB = 2 : 3, use the section formula.

The x-coordinate of C is `(32 + 25)/(2 + 3) = (6 + 10)/5 = 16/5` and the y-coordinate is `(36 + 21)/5 = 4`, which matches the given y.

Hence, `k = 16/5`.