Question

If the point \(\mathrm{R}(k, 4)\) divides the line segment joining the points \(\mathrm{P}(2,6)\) and \(\mathrm{Q}(5, 1)\) in the ratio 2 : 3, then the value of (k) is ______.

Options

• –5

• \(-\frac{16}{5}\)

• 5

• \(\frac{16}{5}\)

Answer 1

If the point \(\mathrm{R}(k, 4)\) divides the line segment joining the points \(\mathrm{P}(2,6)\) and \(\mathrm{Q}(5, 1)\) in the ratio 2 : 3, then the value of (k) is `underlinebb(16/5)`.

Explanation:

With \(m = 2, n = 3\): 

$$x = \frac{2 \times 5 + 3 \times 2}{5} = \frac{16}{5}$$

$$y = \frac{2 \times 1 + 3 \times 6}{5} = 4$$

Hence \(k = \frac{16}{5}\).