Question

points r, s, and t are collinear, point s lies between r and t. find rt if: rs = 2x + 9; st = 7, and rt = x + 12

Explanation:

Step1: Use segment addition postulate

Since \( R, S, T \) are collinear and \( S \) is between \( R \) and \( T \), we have \( RS + ST = RT \). Substitute the given expressions: \( (2x + 9) + 7 = x + 12 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 2x + 16 = x + 12 \). Subtract \( x \) and 16 from both sides: \( 2x - x = 12 - 16 \), so \( x = -4 \).

Step3: Find \( RT \)

Substitute \( x = -4 \) into \( RT = x + 12 \): \( RT = -4 + 12 = 8 \).

Answer:

\( 8 \)