(i)

r = a + $\frac{1}{2}$(a - b)

r = $\left(\begin{array}{c}2\\ 3\end{array}\right)$ + $\frac{1}{2}$[$\left(\begin{array}{c}2\\ 3\end{array}\right)$ - $\left(\begin{array}{c}4\\ 5\end{array}\right)$) ]

r = $\left(\begin{array}{c}2\\ 3\end{array}\right)$ + $\frac{1}{2}$$\left(\begin{array}{c}\mathrm{2\; -\; 4}\\ \mathrm{3\; -\; 5}\end{array}\right)$

r = $\left(\begin{array}{c}2\\ 3\end{array}\right)$ + $\frac{1}{2}$$\left(\begin{array}{c}-2\\ -2\end{array}\right)$

r = $\left(\begin{array}{c}2\\ 3\end{array}\right)$ + $\left(\begin{array}{c}-2x\frac{1}{2}\\ -2x\frac{1}{2}\end{array}\right)$

r = $\left(\begin{array}{c}2\\ 3\end{array}\right)$ + $\left(\begin{array}{c}-1\\ -1\end{array}\right)$

r = $\left(\begin{array}{c}\mathrm{2\; +\; -1}\\ \mathrm{3\; +\; -1}\end{array}\right)$

r = $\left(\begin{array}{c}\mathrm{2\; -\; 1}\\ \mathrm{3\; -\; 1}\end{array}\right)$

r = $\left(\begin{array}{c}1\\ 2\end{array}\right)$

(ii)

|r| = $\sqrt{1^2\mathrm{+}{2}^2}$

|r| = $\sqrt{1\mathrm{+}4}$

|r| = $\sqrt{5}$ units