Question

If b is the midpoint of ac, ab=12x+11 and bc= 14x - 1, find AB

Answer 1

Answer:

AB = 83

Step-by-step explanation:

The mid-point of any segment divides the segment into two equal parts

∵ B is the midpoint of segment AC

→ That means B divides AC into two equal segments AB and BC

∴ AB = BC

∵ AB = 12x + 11

∵ BC = 14x - 1

→ Equate them

∴ 14x - 1 = 12x + 11

→ Subtract 12x from both sides

∵ 14x - 12x - 1 = 12x - 12x + 11

∴ 2x - 1 = 11

→ Add 1 to both sides

∵ 2x - 1 + 1 = 11 + 1

∴ 2x = 12

→ Divide both sides by 2

∵ $\frac{2x}{2}=\frac{12}{2}$

∴ x = 6

→ To find AB substitute x by 6 in its expression

∵ ab = 12x + 11

∵ x = 6

∴ AB = 12(6) + 11

∴ AB = 72 + 11

∴ AB = 83