Answer/Step-by-step explanation:
AB = 3x - 18
BC = 2x - 21
AC = 39
Since points A, B, and C are collinear,
AB + BC = AC (segment addition postulate)
(3x - 18) + (2x - 21) = 39 (substitution)
Use the equation to solve for x.
3x - 18 + 2x - 21 = 39
Collect like terms
3x + 2x - 18 - 21 = 39
5x - 39 = 39
Add 39 to both sides
5x = 39 + 39
5x = 78
Divide both sides by 5
x = 15.6
AB = 3x - 18
Substitute for x = 15.6 in the expression
AB = 3(15.6) - 18
AB = 28.8
BC = 2x - 21
BC = 2(15.6) - 21
BC = 10.2
B is not the midpoint of segment AC because AB ≠ BC. Or neither AB nor BC = ½ of AC.
