Line m contains the points, a(–2, 6) and b(4, 8), while line n contains the c(8, 12) and d(x, 24). given m and n are perpendicular lines, solve for the value of x. given m and n are parallel lines, solve for the value of x. in your final answer, include all formulas and calculations necessary to solve for x.

Find the slope of AB...m=(y2-y1)/(x2-x1) in this case:

m=(8-6)/(4--2)

m=2/6

m=1/3

For CD to be perpendicular to AB it must have the negative reciprocal of the slope of AB, mathematically:

m1*m2=-1  for lines to be perpendicular, in this case

m/3=-1

m=-3  So CD will have a slope of -3

CD then can be expressed as part of the line:

y=-3x+b, we can solve for b using point C, (8,12)...

12=-3(8)+b

12=-24+b

36=b so the line that CD is on is:

y=-3x+36  

We want to know the x coordinate for (x,24), so y=24

24=-3x+36

3x+24=36

3x=12

x=4