Maria starts at the origin and walks along all of the vector $2 extbf{i} + 3 extbf{j}$, then walks along all of the vector $3 extbf{i} - 2 extbf{j}$ and finally along all of the vector $4 extbf{i} - 3 extbf{j}$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2020 - Paper 1

From $(2, 3)$, walking along the vector $3\textbf{i} - 2\textbf{j}$ brings her to [(2 + 3, 3 - 2) = (5, 1)].

From $(5, 1)$, walking along the vector $4\textbf{i} - 3\textbf{j}$ results in [(5 + 4, 1 - 3) = (9, -2)].

The distance from the origin to the point $(9, -2)$ can be calculated using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substituting $(x_1, y_1) = (0, 0)$ and $(x_2, y_2) = (9, -2)$, we get: $d = \sqrt{(9 - 0)^2 + (-2 - 0)^2} = \sqrt{81 + 4} = \sqrt{85}$