Question

question 3 (2 points)
given that b is the midpoint of segment ac. if ab = 3x + 9 and bc = x + 21, find x and ac.
draw a picture and label the information to help you get started.
*remember: the midpoint divides the segment into 2 equal parts. do not use the segment addition postulate to solve for x.
x =
ac =

Explanation:

Step1: Set AB equal to BC

Since B is the mid - point of AC, AB = BC. So, $3x + 9=x + 21$.

Step2: Solve for x

Subtract x from both sides: $3x - x+9=x - x + 21$, which simplifies to $2x+9 = 21$. Then subtract 9 from both sides: $2x+9 - 9=21 - 9$, giving $2x=12$. Divide both sides by 2: $\frac{2x}{2}=\frac{12}{2}$, so $x = 6$.

Step3: Find the length of AB or BC

Substitute x = 6 into the expression for AB: $AB=3x + 9=3\times6+9=18 + 9=27$. Since BC is equal to AB, BC = 27.

Step4: Find the length of AC

Since AC=AB + BC and AB = BC = 27, then $AC=27+27 = 54$.

Answer:

$x = 6$
$AC = 54$