Question

The equation of straight line equally inclined to the axes and equidistant from the point $(1,-2)$ and $(3,4)$ is

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

Answer 1

The correct option is B $y-x-1=0$

Equally inclined to the axes, means that the slope of the line must be: $m=1$ [parallel to $y=x$]
the line pases through the midpoint of the segment joining $(-3,-2)$ and $(3,4)$
midpoint is: $(\frac{3-3}{2},\frac{4-2}{2})=(0,1)$
point-slope form:$(y-1)=m(x-0)$
$y-1=1\times x$
i.e.$x-y+1=0$