Question

1. if s is the midpoint of \\(\overline{rt}\\), \\(rs = 5x + 17\\), and \\(st = 8x - 31\\), find \\(rs\\).

Explanation:

Step1: Use midpoint property (RS = ST)

Since \( S \) is the midpoint of \( \overline{RT} \), \( RS = ST \). So we set up the equation:
\( 5x + 17 = 8x - 31 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\( 17 = 3x - 31 \)
Add 31 to both sides:
\( 48 = 3x \)
Divide both sides by 3:
\( x = 16 \)

Step3: Find \( RS \) by substituting \( x \)

Substitute \( x = 16 \) into \( RS = 5x + 17 \):
\( RS = 5(16) + 17 \)
\( RS = 80 + 17 \)
\( RS = 97 \)

Answer:

\( 97 \)