\(2\sqrt{2}\)
\(\sqrt{13}\)
\(5\)
\(\sqrt{29}\)
Correct answer is D
\(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} , q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\)
\(\frac{1}{2}p = \begin{pmatrix} 1 \\ -1 \end{pmatrix}\)
\(q - \frac{1}{2}p = \begin{pmatrix} 3 \\ 4 \end{pmatrix} - \begin{pmatrix} 1 \\ -1 \end{pmatrix} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}\)
\(|q - \frac{1}{2}p| = \sqrt{2^{2} + 5^{2}} = \sqrt{29}\)