Điểm A biểu diễn số phức z khác 0, điểm B biểu diễn số phức w.

* Hướng dẫn giải

Đáp án B

$$\begin{gathered} \mathrm{Đặt} \mathrm{z}=\mathrm{a}+\mathrm{bi} \left(\mathrm{a};\mathrm{b}\in \mathrm{ℝ}\right)\Rightarrow \mathrm{Điểm} \mathrm{biểu} \mathrm{diễn} \mathrm{z} \mathrm{là} \mathrm{A} \left(\mathrm{a};\mathrm{b}\right) \\ \mathrm{w}=\frac{\left(1-\mathrm{i}\right)\mathrm{z}}{2}=\frac{\left(1-\mathrm{i}\right)(\mathrm{a}+\mathrm{bi})}{2}=\frac{\mathrm{a}+\mathrm{b}}{2}+\mathrm{i}.\frac{\mathrm{b}-\mathrm{a}}{2} \\ \Rightarrow \mathrm{Điểm} \mathrm{biểu} \mathrm{diễn} \mathrm{w} \mathrm{là} \mathrm{B}\left(\frac{\mathrm{a}+\mathrm{b}}{2};\frac{\mathrm{b}-\mathrm{a}}{2}\right) \\ \mathrm{Ta} \mathrm{có}: \\ \overrightarrow{\mathrm{AB}}=\left(\frac{\mathrm{b}-\mathrm{a}}{2};\frac{-\mathrm{a}-\mathrm{b}}{2}\right) \\ \Rightarrow \mathrm{AB}=\sqrt{{\left(\frac{\mathrm{b}-\mathrm{a}}{2}\right)}^2+{\left(\frac{-\mathrm{a}-\mathrm{b}}{2}\right)}^2}=\sqrt{\frac{{\left(\mathrm{a}-\mathrm{b}\right)}^2}{4}+\frac{{\left(\mathrm{a}+\mathrm{b}\right)}^2}{4}} \\ \overrightarrow{\mathrm{OB}}=\left(\frac{\mathrm{a}+\mathrm{b}}{2};\frac{\mathrm{b}-\mathrm{a}}{2}\right) \\ \Rightarrow \mathrm{OB}=\sqrt{{\left(\frac{\mathrm{a}+\mathrm{b}}{2}\right)}^2+{\left(\frac{\mathrm{b}-\mathrm{a}}{2}\right)}^2}=\sqrt{\frac{{\left(\mathrm{a}-\mathrm{b}\right)}^2}{4}+\frac{{\left(\mathrm{a}+\mathrm{b}\right)}^2}{4}} \\ \Rightarrow △\mathrm{OAB} \mathrm{cân} \mathrm{tại} \mathrm{B} \left(1\right) \\ \mathrm{Mặt} \mathrm{khác}: \\ \overrightarrow{\mathrm{AB}}.\overrightarrow{\mathrm{BO}}=\frac{\mathrm{b}-\mathrm{a}}{2}.\frac{-\left(\mathrm{a}+\mathrm{b}\right)}{2}+\frac{-\mathrm{a}-\mathrm{b}}{2}.\frac{\mathrm{a}-\mathrm{b}}{2}=-\frac{{\mathrm{b}}^2-{\mathrm{a}}^2}{4}+\frac{-\left({\mathrm{a}}^2-{\mathrm{b}}^2\right)}{4} \\ =\frac{{\mathrm{a}}^2-{\mathrm{b}}^2-{\mathrm{a}}^2+{\mathrm{b}}^2}{4}=0 \\ \Rightarrow △\mathrm{OAB} \mathrm{vuông} \mathrm{tại} \mathrm{B} \left(2\right) \\ \mathrm{Từ} \left(1\right) \mathrm{và} \left(2\right) \Rightarrow △\mathrm{OAB} \mathrm{vuông} \mathrm{cân} \mathrm{tại} \mathrm{B} \end{gathered}$$