Question

s is the midpoint of \\(\overline{rt}\\). if \\(rs = x + 3\\) and \\(rt = 6x + 2\\), what is \\(rs\\)? 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 \( RT = 2 \times RS \). Substituting the given expressions, we get \( 6x + 2 = 2(x + 3) \).

Step2: Solve for \( x \)

Expand the right side: \( 6x + 2 = 2x + 6 \). Subtract \( 2x \) from both sides: \( 4x + 2 = 6 \). Subtract 2 from both sides: \( 4x = 4 \). Divide by 4: \( x = 1 \).

Step3: Find \( RS \)

Substitute \( x = 1 \) into \( RS = x + 3 \): \( RS = 1 + 3 = 4 \).

Answer:

\( 4 \)