Question

b is the midpoint of \\(\overline{ac}\\). \\(bc = 47\\) and \\(ac = y - 7\\). find \\(y\\), \\(ab\\), and \\(ac\\).

Explanation:

Step1: Recall midpoint property

Since B is the midpoint of \( \overline{AC} \), \( AB = BC \) and \( AC = AB + BC = 2 \times BC \).
Given \( BC = 47 \), so \( AB = 47 \) and \( AC = 2 \times 47 = 94 \).

Step2: Solve for y

We know \( AC = y - 7 \) and \( AC = 94 \). So set up the equation:
\( y - 7 = 94 \)
Add 7 to both sides:
\( y = 94 + 7 = 101 \)

Answer:

\( y = 101 \), \( AB = 47 \), \( AC = 94 \)