Cho đường thẳng d:

- Hướng dẫn giải

$$\begin{gathered} d \cap Oy=\left\{B\right\}\text{⇒} x_B =0\Rightarrow y_B =m-1 \Rightarrow B\left(0;m-1\right) \Rightarrow OB=\left|m-1\right| \\ d \cap Ox=\left\{A\right\} \Rightarrow y_A =0 \Rightarrow m{x}_A +m-1=0 \iff x_A=\frac{{\displaystyle 1-m}}{{\displaystyle m}}\left(m\ne 0\right) \end{gathered}$$

 $\Rightarrow A\left(\frac{1-m}{m};0\right)\Rightarrow OA=\left|\frac{1-m}{m}\right|$

Tam giác OAB vuông cân tại O

$$\begin{gathered} OA = OB\iff \left|m-1\right|=\left|\frac{1-m}{m}\right| \\ \iff \left[\begin{array}{l}m-1=\frac{1-m}{m}\\ m-1=\frac{m-1}{m}\end{array}\right.\iff \left[\begin{array}{l}{m}^2=1\\ \left(m-1\right)\left(1-\frac{1}{m}\right)=0\end{array}\right. \end{gathered}$$

 $\iff \left[\begin{array}{l}m=\pm 1\\ \frac{{\left(m-1\right)}^2}{m}=0\end{array}\right.\iff m=\pm 1$

Đáp án cần chọn là: D