If A=(0,-17), B=(4,-5), and C=(12, -1), what is the length of the altitude from C to AB
there are several ways to attack this problem. One is to get the equation of the line perpendicular to AB which passes through C. If the intersection is at P, the the altitude is CP
line through A,B
(y+17) /x = (12/4) = 3
y = 3x - 17
slope of that line is 3, so slope of ┴ is -1/3
line through C with slope -1/3 is
(y+1) = -1/3 (x-12)
y = -1/3 x + 3
The lines intersect at (6,1)
length of CP = √(6^2 + 2^2) = 2√10