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

Answers (1)

Given :

$P=(x_1,y_1)=(2,-2)$

$Q=(x_2,y_2)=(3,7)$

$R=(x_3,y_3)=\left ( \frac{24}{11},y \right )$

Let

$\frac{PR}{QR}=\frac{k}{1}$

$R(x,y)=\left ( \frac{kx_2+x_1}{k+1},\frac{ky_2+y_1}{k+1} \right )$

$\frac{24}{11}=\frac{k\times 3+2}{k+1}$ (comparing the x coordinate)

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

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

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

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

Now for the y coordinate of R :

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

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

$=\frac{14-2\times 9}{11}$

$=\frac{14-18}{11}$

$=\frac{-4}{11}$

$R=\left ( \frac{24}{11},\frac{-4}{11} \right )$

Posted by

Ravindra Pindel

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