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

#### Video Explanation

#### Explanatory Answer

Let the ratio in which (\\frac{24}{11}), y) divides the line segment PQ be m : n

If a point k(x, y) divides a segment joining points A(x_{1}, y_{1}) and B (x_{2}, y_{2}) in the ratio m : n, then

x = \\frac {m{x}_{2}+n{x}_{1}} {m+n}) and y = \\frac {m{y}_{2}+n{y}_{1}} {m+n})

So, the x-coordinate \\frac{24}{11}) = \\frac{m(3) + n(2)}{m + n}))

Or 24m + 24n = 33m + 22n

Or 2n = 9m

Or \\frac{m}{n}) = \\frac{2}{9})

Therefore, m : n = 2 : 9

The ratio in which the point (\\frac{24}{11}), y) divides the line segment PQ is 2 : 9.

The y coordinate of the point = \\frac {m{y}_{2}+n{y}_{1}} {m+n})

Or y = \\frac{(2(7) + 9(-2)}{2+9}) = \\frac{14 - 18}{11}) = -\\frac{4}{11})