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

Options

A. a = 1, b = -1, c = 3
B. a = 1, b = -1, c = -3
C. a = 1, b = 1, c = -3
D. None of these

Answer

C

Explanation

The equation of straight line equally inclined to the axes is `(x)/(a)+(y)/(a)=1impliesx+y=a`. Since, it is equidistant from the points `(1,-2)` and (3, 4), so perpendicular distances from these points on the line will be equal.
`implies(|1-2-a|)/(sqrt(1^(2)+1^(1)))=(|3+4-a|)/(sqrt(1^(2)+1^(2)))`
`implies1+a^(2)+2a=49+a^(2)-14a`
`implies" "16a=48impliesa=3`
`:.` Equation is `x+y-3=0`.
But given equation is
`ax+by+c=0`.
`:.a=1,b=1,c=-3`