Find the equation of the right bisector of the line segment joining the points \((3,4)\) and \((-1,2)\).

The right angle bisector of the line segment joining points \(A(3,4)\) and \(B(-1,2)\) passes through the mid-point of \(A\) and \(B\) perpendicular to line segment \(A B\). Now, the mid-point of \(A(3,4)\) and \(B(-1,2)\) is \(M\left(\frac{3-1}{2}, \frac{4+2}{2}\right)=M(1,3)\) and slope of right angle bisector is \(=-\frac{3-(-1)}{4-2}=-2\) \(\therefore\) Equation of required right angle bisector is \(\begin{aligned} y-3 & =-2(x-1) \\ \Rightarrow \quad 2 x+y & =5 \text { or } 2 x+y-5=0 \end{aligned}\) Hence, option (a) is correct.