My fist step to solving this question would be to find the mid-point of the given line.
The mid point of (4,1) and (2,-5) is (3,-2). The mid point is where the perpendicular bisector connects or bisects the given segment.
My second step would be to graph the two given points and to connect them, forming a line. This way, I would know the slope of the line and then I would be able to find the slope of the perpendicular bisector, since the slope for perpendicular lines is the opposite reciprocal of the given line.
In doing this, I discovered that the slope of the segment with the given endpoints is 3 which means that the slope of the perpendicular bisector will be -1/3.
So, so far we've got a point of intersection and a slope which is all we need to formulate the equation of the line that we are looking for.
In the end, our answer will be y= -1/3x - 1.