Cho đường thẳng d:

- Hướng dẫn giải

$$\begin{gathered} d \cap Oy=\left\{B\right\}\text{⇒} x_B =0\Rightarrow y_B =-1 \Rightarrow B\left(0;-1\right) \Rightarrow OB=\left|-1\right|=1 \\ d\cap Ox=\left\{A\right\}\text{⇒} y_A =0 \iff \left(k–2\right)x_A -1=0 \iff x_A=\frac{{\displaystyle 1}}{{\displaystyle k-2}}\left(k\ne 2\right) \end{gathered}$$

 $\Rightarrow A\left(\frac{1}{k-2};0\right)\Rightarrow OA=\left|\frac{1}{k-2}\right|$

 $\begin{array}{l}{S}_{\Delta AOB}=\frac{1}{2}OA.OB=1\iff \frac{1}{2}\mathrm{.1.}\left|\frac{1}{k-2}\right|=1\\ \iff |k-2|=\frac{1}{2}\iff \left[\begin{array}{l}k=\frac{5}{2}\\ k=\frac{3}{2}\end{array}\right.\end{array}$(tmdk)

Đáp án cần chọn là: D