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.

Open in App

Solution

Let point R divides PQ in the ratio k:1

R = $(\frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}})$

$\Rightarrow (\frac{24}{11}, y) = (\frac{k (3) + 1 (2)}{k + 1}, \frac{k (7) + 1 (- 2)}{k + 1})$

= $(\frac{3 k + 2}{k + 1}, \frac{7 k - 2}{k + 1})$

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

$\Rightarrow 11 (3 k + 2) = 24 (k + 1)$

$\Rightarrow 33 k + 22 = 24 k + 24$

$\Rightarrow 33 k - 24 k = 24 - 22$

$\Rightarrow 9 k = 2 \Rightarrow k = \frac{2}{9}$

$∴ k : 1 = 2 : 9$

Now,

y = $\frac{7 k - 2}{k + 1} = \frac{7 (\frac{2}{9}) - 2}{\frac{2}{9} + 1}$

= $\frac{\frac{14}{9} - 2}{\frac{2}{9} + 1} = \frac{\frac{14 - 18}{9}}{\frac{2 + 9}{9}} = \frac{- 4}{11}$

Line PQ divides in the ratio 2:9 and value of y = $\frac{- 4}{11}$

Suggest Corrections

134

Similar questions

(\frac{24}{11}, y)

x - y - 2 = 0

(3, - 1)

(8, 9)

y

P (5, 7)

Q (- 8, 9)

Join BYJU'S Learning Program