1. **State the problem:** We need to find the image of a triangle ABC under reflection across the x-axis. 2. **Recall the reflection rule:** Reflecting a point $(x,y)$ across the x-axis results in the point $(x,-y)$. 3. **Apply the transformation to each vertex:** - Point $A$ lies on the x-axis, so if $A=(x,0)$, then $A'=(x,-0)=(x,0)$, so $A'$ remains on the x-axis. - Point $B$ is above the x-axis at $(x,y)$ with $y>0$, so $B'=(x,-y)$ is the point directly below $B$. - Point $C$ lies on the x-axis, so $C'=(x,0)$ remains on the x-axis. 4. **Conclusion:** The reflected triangle $A'B'C'$ is the mirror image of $ABC$ below the x-axis, with $A'$ and $C'$ on the x-axis and $B'$ directly below $B$. $$\text{If } A=(x_A,0), B=(x_B,y_B), C=(x_C,0), \text{ then } A'=(x_A,0), B'=(x_B,-y_B), C'=(x_C,0).$$