Question

The equation of the line cutting off intercepts on the axes of coordinates equal in magnitude but opposite in sign and passing through the point $(2,3)$

• A. $x-y+1=0$
• B. $x+y-5=0$
• C. $2x-y-7=0$
• D. $1x-y-1=0$

Answer 1

The correct option is A $x-y+1=0$

Equation of a line by intercept form is

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

where

a=x-intercept

b=y-intercept

But given that x and y intercept are equal in magnitude but opposite in sign

$\therefore a=-borb=-a$

Thus, equation of line is

$\frac{x}{a}-\frac{y}{a}=1$

$x-y=a$

$x-y-a=\mathrm{0......}\left(1\right)$

Since the line is passing through (2,3)

$\therefore$ Point (2,3) will satisfy equation of line

Putting $x=2$ and $y=3$ in (1)

$2-3-a=0$

$-1-a=0$

$a=-1$

Now, equation of line become

$x-y+1=0$

This is the required equation.