Question

B is the midpoint of AC. What is the length of AB? AB is 9x+7 and BC is -3x+20

Answer 1

Answer:

$AB = \frac{67}{4}$

Step-by-step explanation:

If $B$ is the midpoint of $\overline{AC}$ then $AB$ is just half of $AC$ and also, $BC$ is just half of $AC$. This means that $AB$ must be equal to $BC$. Essentially, $9x +7 = -3x +20$ and we can solve for the of $x$ from that equation.

$9x +7 = -3x +20 \\ 9x +7 +3x = -3x +20 +3x \\ 12x +7 = 20 \\ 12x +7 -7 = 20 -7 \\ 12x = 13 \\ \frac{12x}{12} = \frac{13}{12} \\ x = \frac{13}{12}$

Now we can solve for $AB$

$AB = 9(\frac{13}{12}) +7 \\ AB = 3(\frac{13}{4}) +7 \\ AB = \frac{39}{4} +7 \\ AB = \frac{39}{4} +\frac{28}{4} \\ AB = \frac{67}{4}$