In what ratio does the point (24/11, y) divide the line segment joining the points P(2, - 2) and Q(3, 7)

In what ratio does the point (24/11, y) divide the line segment joining the points P(2, -2) and Q(3, 7) ? Also find the value of y.

Answer

Let PA : AQ = k : 1

$$ \frac{2+3k}{k+1} = \frac{24}{11} $$

$$ K = \frac{2}{9} $$

Hence, the ratio is 2 : 9

$$ y  = \frac{-18+14}{11} = \frac{-4}{11} $$