Question

If a point \(\mathrm{R}\left(\frac{23}{5}, \frac{33}{5}\right)\) divides the line segment PQ joining the points \(\mathrm{P}(3, 5)\) and \(\mathrm{Q}(x, y)\) in the ratio 2 : 3 internally, then the values of x and y respectively are ______.

Options

• 4, 7

• 5, 9

• 7, 8

• 7, 9

Answer 1

If a point \(\mathrm{R}\left(\frac{23}{5}, \frac{33}{5}\right)\) divides the line segment PQ joining the points \(\mathrm{P}(3, 5)\) and \(\mathrm{Q}(x, y)\) in the ratio 2 : 3 internally, then the values of x and y respectively are 7, 9.

Explanation:

With \(m = 2, n = 3\):

\(\frac{2x + 3(3)}{5} = \frac{23}{5}\)

\(\Rightarrow 2x = 14\)

\(\Rightarrow x = 7\) 

And \(\frac{2y + 3(5)}{5} = \frac{33}{5}\)

\(\Rightarrow 2y = 18\)

\(\Rightarrow y = 9\)