B is the midpoint of AC. AB =25 and AC= 8x+2 . Find x , BC, and AC.

Answer 1

If AC = 8x+2, and B is the midpoint of AC, and AB=25, then if you doubled that value (50) it would be equal to the length of AC. So...

AC = 50 = 8x + 2

50 = 8x + 2, solve for x

x = 48/8 = 6

X = 6

BC = 25 (definition of midpoint)

AC = 50 (you can either use the definition of midpoint and double it, or plug x into the AC equation).

I hope this helps!

Answer 2

Hello, Celeste,

Since B is the midpoint of line AC, and we know that segment AB = 25, then it must be true that segment BC must also be equal to 25. Since we know the total length (AC) is the sum of AB and BC, then AC = 50.

We are told that segment AC is also equal to 8x + 2. That means we can state:

50 = 8x + 2

Rearranging, 8x = 48, and x = 6.

Therefore, the answers are

x = 6

BC = 25

AC = 25