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.
Step-by-Step Solution
Key Concept: On $y$-axis, $x = 0 \Rightarrow \dfrac{k(-1) + 1(5)}{k+1} = 0 \Rightarrow -k + 5 = 0 \Rightarrow k = 5 \Rightarrow 5 : 1$. $y = \dfrac{5(-4) + 1(-6)}{6} = -\dfrac{26}{6} = -\dfrac{13}{3}$. Point is $\left(0, -\dfrac{13}{3}\right)$.
$-k + 5 = 0 \Rightarrow k = 5$. Ratio is $5 : 1$. [1.0 Mark]
$y = \dfrac{5(-4) + 1(-6)}{5 + 1} = -\dfrac{26}{6} = -\dfrac{13}{3}$. Point is $\left(0, -\dfrac{13}{3}\right)$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating ratio $5 : 1$: 1.0 Mark
Finding intersection point $(0, -13/3)$: 1.0 Mark
Correct Answer: