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(C) Let the line intersect the coordinate axes at points $A(a, 0)$ and $B(0, b)$.The point $P\left(\frac{1}{2}, \frac{1}{3}\right)$ divides the line s

Vedclass · Accepted Answer

$4x + 9y = 5$

Vedclass · Answer

(C) Let the line intersect the coordinate axes at points $A(a, 0)$ and $B(0, b)$.The point $P\left(\frac{1}{2}, \frac{1}{3}\right)$ divides the line segment $AB$ in the ratio $2: 3$.Using the section formula,the coordinates of $P$ are given by:$P = \left(\frac{2(a) + 3(0)}{2 + 3}, \frac{2(0) + 3(b)}{2 + 3}\right) = \left(\frac{2a}{5}, \frac{3b}{5}\right)$.Given $P = \left(\frac{1}{2}, \frac{1}{3}\right)$,we equate the coordinates:$\frac{2a}{5} = \frac{1}{2} \Rightarrow a = \frac{5}{4}$$\frac{3b}{5} = \frac{1}{3} \Rightarrow b = \frac{5}{9}$The intercept form of the line equation is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values of $a$ and $b$:$\frac{x}{5/4} + \frac{y}{5/9} = 1$$\frac{4x}{5} + \frac{9y}{5} = 1$$4x + 9y = 5$.

An equation of a line whose segment between the coordinate axes is divided by the point $\left(\frac{1}{2}, \frac{1}{3}\right)$ in the ratio $2: 3$ is

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