Cho đường thẳng d: y = (2m + 1) x – 1. Tìm m để d cắt 2 trục tọa độ

* Hướng dẫn giải

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

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

$\begin{array}{l}{S}_{\Delta AOB}=\frac{1}{2}OA.OB=\frac{1}{2}\mathrm{.1.}\left|\frac{1}{2m+1}\right|=\frac{1}{2}\\ \iff |2m+1|=1\iff \left[\begin{array}{l}m=0\\ m=-1\end{array}\right.\end{array}$

Đáp án cần chọn là: D