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

Explanation

Let the required equation in intercept form be `\frac{x}{a}+\frac{y}{b}=1`

Therefore, its x- intercept is `a` and y- intercept is `b`

`\implies A(a,0)` and `B(0,b)` is on the given line.

And it is given the point `(h,k)` divides the line segment `A(a,0)` and `B(0,b)` in the ratio `1:2`.

By section formula,

`(h,k)=(\frac{1\times0+2\timesa}{3},\frac{1\times b+2\times 0}{3})`

`\implies(h,k)=(\frac{2a}{3},\frac{b}{3})`

`\implies 2a=3h` and `b=3k`

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