Question

the point b is the mid - point of $overline{ac}$. find the location of a. location of a:

Explanation:

Step1: Recall mid - point formula

If $B$ is the mid - point of $\overline{AC}$, and the coordinates of $B$ is $x_B$, $A$ is $x_A$ and $C$ is $x_C$, then $x_B=\frac{x_A + x_C}{2}$.

Step2: Rearrange the formula to find $x_A$

We know $x_B=- 14$ and $x_C = 12$. Rearranging the mid - point formula gives $x_A=2x_B - x_C$.

Step3: Substitute the values

Substitute $x_B=-14$ and $x_C = 12$ into the formula: $x_A=2\times(-14)-12$.

Step4: Calculate the value of $x_A$

First, calculate $2\times(-14)=-28$. Then, $-28-12=-40$.

Answer:

$-40$