Given a line segment that contains the points a, b, & c in order, and given b is the midpoint of ac, if ab = 10x - 8, and bc = 5x + 17, find x.

If b is the midpoint, that means AB and BC are the same lengths, so 10x-8=5x+17. Subtract 5x from both sides: 5x-8=17. 
Add 8 to both sides: 5x=25
Divide by 5 and find that x=5.

12+3b -1=-5-b -12-1+5=-b-3b -8=-4b

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.