+35 The "perpendicular bisector" of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{AB}$ and is perpendicular to $\overline{AB}$. The equation of the perpendicular bisector of the line segment joining the points $(1,2)$ and $(-5,12)$ is $y = mx + b$. Find $m+b$.
The midpoint of the line segment joining the points (1,2) and (-5,12) is:
M = (1 - 5)/2, (2 + 12)/2 = -2, 7
The slope of the line joining the points (1,2) and (-5,12) is:
(12 - 2)/(-5 - 1) = -10/-6 = 5/3
The slope of the perpendicular bisector is the negative reciprocal of the slope of the line joining the points (1,2) and (-5,12), which is -3/5.
The equation of the perpendicular bisector is:
y - 7 = -3/5(x + 2)
Solving for m and b, we get m = -3/5 and b = 16/5.
Therefore, m + b = -3/5 + 16/5 = 13/5.
So the answer is 13/5
