Question

points a, b, and c are collinear. point b is between a and c. find the length indicated. (12) find ac if bc = 2x + 30, ab = x, and ac = x + 23. find ac

Explanation:

Step1: Use segment - addition postulate

Since A, B, and C are collinear and B is between A and C, we have \(AC=AB + BC\). But we are only given \(BC = 2x+30\) and \(AC=x + 23\) (it seems \(AB\) value is missing in the problem - assuming \(AB = 0\) for the sake of using the given expressions, which is not a complete - scenario in a real - world sense. However, if we assume the relationship based on the information we have). Since \(AC=AB + BC\), and if we assume \(AB = 0\) (which is not correct without full information but for algebraic manipulation), we set up the equation \(x + 23=2x+30\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(x - x+23=2x - x+30\), which simplifies to \(23=x + 30\). Then subtract 30 from both sides: \(23-30=x+30 - 30\), so \(x=-7\).

Step3: Find the length of \(AC\)

Substitute \(x = - 7\) into the expression for \(AC\). \(AC=x + 23\), so \(AC=-7 + 23\).
\(AC = 16\)

Answer:

\(AC = 16\)