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 \(A\), \(B\), and \(C\) are \(x_A\), \(x_B\), and \(x_C\) respectively, then \(x_B=\frac{x_A + x_C}{2}\).

Step2: Rearrange formula to solve for \(x_A\)

We know \(x_B = 5\) and \(x_C=19\). Rearranging the mid - point formula \(x_B=\frac{x_A + x_C}{2}\) gives \(2x_B=x_A + x_C\), and then \(x_A=2x_B - x_C\).

Step3: Substitute values

Substitute \(x_B = 5\) and \(x_C = 19\) into the formula \(x_A=2x_B - x_C\). So \(x_A=2\times5-19\).

Step4: Calculate result

\(x_A = 10 - 19=-9\).

Answer:

\(-9\)