Question

s is the midpoint of \\(\overline{rt}\\). if \\(st = 2x + 1\\) and \\(rt = 5x + 1\\), what is \\(st\\)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( S \) is the midpoint of \( \overline{RT} \), we know that \( RT = 2 \times ST \). Substitute the given expressions: \( 5x + 1 = 2(2x + 1) \).

Step2: Solve for \( x \)

Expand the right side: \( 5x + 1 = 4x + 2 \). Subtract \( 4x \) from both sides: \( x + 1 = 2 \). Then subtract 1 from both sides: \( x = 1 \).

Step3: Find \( ST \)

Substitute \( x = 1 \) into \( ST = 2x + 1 \): \( ST = 2(1) + 1 = 3 \).

Answer:

\( 3 \)