Find the ratio in which the line segment joining $A(1, -5)$ and $B(-4, 5)$ is divided by the $x$-axis. Also find the coordinates of the point of division.
Step-by-Step Solution
Key Concept: Let ratio be $k : 1$. On the x-axis, $y$-coordinate is $0$.
Let ratio be $k : 1$ and point of division be $P(x, 0)$.
$y = \dfrac{k(5) + 1(-5)}{k + 1} = 0 \Rightarrow 5k - 5 = 0 \Rightarrow k = 1$. Ratio is $1 : 1$. [1.0 Mark]
Now $x = \dfrac{1(-4) + 1(1)}{1 + 1} = \dfrac{-3}{2}$. Coordinates of point of division are $\left(-\dfrac{3}{2}, 0\right)$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding ratio $k = 1$ ($1:1$): 1.0 Mark
Finding x-coordinate $(-3/2)$ and point $(-3/2, 0)$: 1.0 Mark
Correct Answer: