Question

point o is on line segment (overline{np}). given (np = 3x), (no = 2x), and (op = 8), determine the numerical length of (overline{no}).

Explanation:

Step1: Use the segment - addition postulate

Since \(O\) is on \(\overline{NP}\), then \(NP = NO+OP\).
Substitute the given expressions: \(3x=2x + 8\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides of the equation \(3x=2x + 8\).
\(3x-2x=2x + 8-2x\), so \(x = 8\).

Step3: Find the length of \(\overline{NO}\)

Since \(NO = 2x\) and \(x = 8\), then \(NO=2\times8\).

Answer:

\(16\)