Find the equation of the perpendicular bisector of the line segment joining the points A(1, 2) and B(3, 8).
Answer: A
The perpendicular bisector passes through the midpoint of AB and has a slope that is the negative reciprocal of the slope of AB.
1. Find the midpoint of AB: \((\frac{1+3}{2}, \frac{2+8}{2}) = (2, 5)\).
2. Find the slope of AB: \(m_{AB} = \frac{8-2}{3-1} = \frac{6}{2} = 3\).
3. Find the slope of the perpendicular bisector: \(m_{perp} = -1/3\).
4. Use the point-slope form with the midpoint (2, 5) and slope -1/3:
y - 5 = -1/3 (x - 2)
3(y - 5) = -1(x - 2)
3y - 15 = -x + 2
x + 3y = 17.