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Find the ratio in which the y-axis divides the line segment joining the points $(5, - 6)$ and $(- 1, - 4)$. Also, find the point of intersection.
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Let the ratio be $k:1$
Point of intersection is $(0,y)$
$0 = \frac{k(-1) + 1(5)}{k+1} \Rightarrow -k+5 = 0 \Rightarrow k=5$
Required ratio is $5:1$
$y = \frac{k(-4) + 1(-6)}{k+1} = \frac{5(-4)+1(-6)}{5+1} = \frac{-20-6}{6} = \frac{-26}{6} = -\frac{13}{3}$
Point of intersection is $(0, -\frac{13}{3})$
Point of intersection is $(0,y)$
$0 = \frac{k(-1) + 1(5)}{k+1} \Rightarrow -k+5 = 0 \Rightarrow k=5$
Required ratio is $5:1$
$y = \frac{k(-4) + 1(-6)}{k+1} = \frac{5(-4)+1(-6)}{5+1} = \frac{-20-6}{6} = \frac{-26}{6} = -\frac{13}{3}$
Point of intersection is $(0, -\frac{13}{3})$