Question

points a, b, and c are collinear. point b is between a and c. find ab if: ac = 3x + 3, ab = -1 + 2x, bc = 11. ab= 13

Explanation:

Step1: Use segment addition postulate

Since \( B \) is between \( A \) and \( C \), \( AC = AB + BC \). Substitute the given expressions: \( 3x + 3 = (-1 + 2x) + 11 \)

Step2: Solve for \( x \)

Simplify the right side: \( 3x + 3 = 2x + 10 \). Subtract \( 2x \) from both sides: \( x + 3 = 10 \). Subtract 3: \( x = 7 \)

Step3: Find \( AB \)

Substitute \( x = 7 \) into \( AB = -1 + 2x \): \( AB = -1 + 2(7) = -1 + 14 = 13 \)

Answer:

13