Question

.\overline{nq}
q 1in. p 1\frac{1}{4}in. n

Explanation:

Step1: Identify segment lengths

The length of $QP = 1$ in and $PN=1\frac{1}{4}=\frac{5}{4}$ in.

Step2: Calculate length of $\overline{NQ}$

By the segment - addition postulate, $NQ=QP + PN$. So $NQ=1+\frac{5}{4}=\frac{4 + 5}{4}=\frac{9}{4}=2\frac{1}{4}$ in.

Answer:

$2\frac{1}{4}$ in