A line passes through the point (3,-2). Find the locus of the middle point of the portion the line intercepted between the axes.

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 `(3,-2)` divides the line segment `A(a,0)` and `B(0,b)` in the ratio `1:1`.

By section formula,

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

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

`\implies a=6` and `b=-4`

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