Question

r is the midpoint of \\(\overline{qs}\\). if \\(rs = 10x + 5\\) and \\(qs = 18x + 12\\), what is \\(rs\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( R \) is the midpoint of \( \overline{QS} \), \( QS = 2 \times RS \). So we have the equation \( 18x + 12 = 2(10x + 5) \).

Step2: Solve for \( x \)

Expand the right side: \( 18x + 12 = 20x + 10 \).
Subtract \( 18x \) from both sides: \( 12 = 2x + 10 \).
Subtract \( 10 \) from both sides: \( 2 = 2x \).
Divide both sides by \( 2 \): \( x = 1 \).

Step3: Find \( RS \)

Substitute \( x = 1 \) into \( RS = 10x + 5 \): \( RS = 10(1) + 5 = 15 \).

Answer:

\( 15 \)