Points A, B, and C are all collinear and AC=94. AB= 7x + 8 BC= 5x + 2. How would I find how long each segment is?

Answer 1

The Segment Addition Postulate says AC = AB + BC so if AC = 94 and AB = 7x + 8 and BC = 5x + 2 then we can substitute those into AC = AB + BC to get:

94 = (7x + 8) + (5x + 2) the combine like-terms to get:

94 = 12x + 10 then subtract 10 from both sides to get:

84 = 12x then divide both sides by 12 to get:

x = 7

Once you know what x is:

AB = 7x + 8 or 7(7) + 8 or AB = 57

BC = 5x + 2 = 5(7) + 2 = 37

Answer 2

Since the points are collinear that means they are on the same straight line . Since AC = 94 , which is the line segment and B is between A and C , then we have

AB+BC= AC

7x+8 +5x+2 = 94 ( simplify like terms )

12x +10 =94 ( substract 10 from both sides )

12X = 84 ( divide by 12 both sides)

x = 7

Now , AB = 7*7 +8 = 57 , BC = 5*7 +2 = 37

Let's validate AC = 94 ( 57+37 = 94 ) TRUE