Find the equation of the line whose portion intercepted between the axes is
Question:

Find the equation of the line whose portion intercepted between the axes is bisected at the point (3, -2).

 

Solution:

To Find: The equation of the line whose portion intercepted between the axes is bisected at the point (3, -2).

Formula used:

Let the equation of the line be

$\frac{x}{a}+\frac{y}{b}=1$

Since it is given that this equation, whose portion is intercepted between the axes is bisected i.e.; is divided into ratio $1: 1$.

Let $A(a, 0)$ and $B(0, b)$ be the points foring the coordinate axis.

$\Rightarrow a$ and $b$ are intercepts of $x$ and $y$-axis respectively.

By using mid-point formula $(\mathrm{m}: \mathrm{n}=1: 1)$

$(x, y)=\left(\frac{y_{1}+x_{1}}{2}, \frac{y_{2}+x_{2}}{2}\right)=\left(\frac{a}{2}, \frac{b}{2}\right)$

Since given point (3 , -2) divides coordinate axis in 1:1 ratio

(x , y) = (3 , -2)

$\Rightarrow \frac{a}{2}=3$ and $\frac{b}{2}=-2$

$a=6 b=-4$

equation of the line $: \frac{x}{a}+\frac{y}{b}=1$

$\frac{x}{6}+\frac{y}{-4}=1$

$-4 x+6 y=-24$

$-2 x+3 y=-12$

Hence the required equation of the line is $2 x-3 y=12$. 

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