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. $y+1=0$
• C. $y=x+2$
• D. $yx+1=0$

Answer 1

The correct option is C $y=x+2$

Line is $y=x+c$
Distance from $(1,-2)$=distance from $(3,-1)$
$\begin{array}{c}\frac{\begin{array}{c}\\ |1+2-c|\end{array}}{\sqrt{2}}=\frac{\begin{array}{c}\\ |4-3-c|\end{array}}{\sqrt{2}}\\ Therefore,c=2\\ \therefore y=x+2\end{array}$