Point R(h, k) divides a line segment between | vedclass

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(A) Let $AB$ be the line segment between the axes such that point $R(h, k)$ divides $AB$ in the ratio $1: 2$. Let the coordinates of $A$ be $(a, 0)$ a

Vedclass · Accepted Answer

$2kx + hy = 3hk$

Vedclass · Answer

(A) Let $AB$ be the line segment between the axes such that point $R(h, k)$ divides $AB$ in the ratio $1: 2$. Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$. Since point $R(h, k)$ divides $AB$ in the ratio $1: 2$,by the section formula: $(h, k) = \left(\frac{1 	imes 0 + 2 	imes a}{1 + 2}, \frac{1 	imes b + 2 	imes 0}{1 + 2}ight) = \left(\frac{2a}{3}, \frac{b}{3}ight)$. Thus,$h = \frac{2a}{3} \Rightarrow a = \frac{3h}{2}$ and $k = \frac{b}{3} \Rightarrow b = 3k$. The equation of the line in intercept form is $\frac{x}{a} + \frac{y}{b} = 1$. Substituting $a$ and $b$: $\frac{x}{3h/2} + \frac{y}{3k} = 1$. $\frac{2x}{3h} + \frac{y}{3k} = 1$. Multiplying by $3hk$: $2kx + hy = 3hk$.

Point $R(h, k)$ divides a line segment between the axes in the ratio $1: 2$. Find the equation of the line.

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