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 \(\overline{NP}\), \(NP = NO+OP\).
Given \(NP = 3x\), \(NO = 2x\), and \(OP = 8\), we substitute into the equation: \(3x=2x + 8\).

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 \(NO\)

Since \(NO = 2x\) and \(x = 8\), then \(NO=2\times8\).
\(NO = 16\).

Answer:

$16$