Final answer:
The equation of the perpendicular bisector is found by determining the slope of the original line and then using the negative reciprocal for the slope of the bisector. The midpoint coordinates are needed to find the exact equation but can be generalized if they are not known.
Step-by-step explanation:
The question is asking us to find the equation of the perpendicular bisector of a line segment AB whose equation is given by x + 4y = 8. The first step is to find the slope of this line, which is -1/4 (since it would be rearranged to y = -1/4x + 2). A perpendicular line would have a slope that is the negative reciprocal of -1/4, so the slope of the perpendicular bisector would be 4. Next, we'll need to find the midpoint of the line segment AB to determine a point through which the perpendicular bisector should pass. However, without the actual coordinates of A and B, we can't calculate the midpoint. As the question provides limited information, we would typically need more data to find the exact equation of the bisector.
Since we don't have specific points for A and B, let's assume the midpoint is at (h, k). The general form of the equation for the perpendicular bisector is then y - k = 4(x - h), or rearranged to the standard form 4x - y - 4h + k = 0.