The ratio in which the x-axis divides the lin | vedclass

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(B) Let the ratio in which the $x$-axis divides the line segment joining the points $A(2, -3)$ and $B(5, 6)$ be $k : 1$.Since the point lies on the $x

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$1 : 2$

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(B) Let the ratio in which the $x$-axis divides the line segment joining the points $A(2, -3)$ and $B(5, 6)$ be $k : 1$.Since the point lies on the $x$-axis,its $y$-coordinate must be $0$.Using the section formula,the $y$-coordinate of the dividing point is given by $\frac{k(6) + 1(-3)}{k + 1} = 0$.Solving for $k$: $6k - 3 = 0$ $\Rightarrow 6k = 3$ $\Rightarrow k = \frac{3}{6} = \frac{1}{2}$.Thus,the ratio is $\frac{1}{2} : 1$,which is $1 : 2$.Alternatively,for a line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ divided by the $x$-axis,the ratio is $-\frac{y_1}{y_2} = -\frac{-3}{6} = \frac{3}{6} = 1 : 2$.

The ratio in which the $x$-axis divides the line segment joining the points $(2, -3)$ and $(5, 6)$ is

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