Question

Reduce the equation $3x-2y+4=0$ to intercepts form and find the length of the segment intercepted between the axes.

Answer 1

We have $3x-2y+4=0$ $\Rightarrow 3x-2y=-4$

$\Rightarrow \frac{3x}{-4}+\frac{y}{2}=1\left[\text{on dividing both sides by -4}\right]$

$\Rightarrow \frac{x}{\left(\frac{-4}{3}\right)}+\frac{y}{2}=1$

$\Rightarrow \frac{x}{a}+\frac{y}{b}=1,a=\frac{-4}{3}andb=1$

$\therefore \frac{x}{\left(\frac{-4}{3}\right)}+\frac{y}{2}=1$

is the required equation in intercepts form.

x-intercept = $\frac{-4}{3}$ and y-intercept = 2

If AB is the part of the line intercepted between the axes then the end points of this line segment are

$A(\frac{-4}{3},0)$ and B (0, 2).

Length AB = $\sqrt{{(\frac{-4}{3}-0)}^2+(0-2{)}^2}=\sqrt{\frac{16}{9}+4}=\frac{2}{3}\sqrt{13}\text{units}$