Final answer:
This question involves reflecting a triangle across the x-axis, and then translating it 2 units up, which is a geometric transformation exercise in Mathematics.
Step-by-step explanation:
The question involves reflections and translations of a triangle on the coordinate plane in Mathematics, specifically in the area of geometry involving transformations. When a figure is reflected across the x-axis, the y-coordinates of the figure's vertices change sign. Following that, translating a figure involves shifting it up, down, left, or right without changing its orientation or size. In this case, the triangle is translated 2 units up, meaning that after the reflection, each y-coordinate of the reflected figure is increased by 2. To visualize the transformation, you can take each vertex of triangle ABC, reflect its y-coordinate over the x-axis to form triangle A'B'C', and then add 2 to each y-coordinate to get the vertices of triangle DEF.
To see this in practice: If a vertex of triangle ABC is at (x, y), its reflected image across the x-axis would be at (x, -y). Then, translating it 2 units up, the coordinates of the corresponding vertex on triangle DEF would be at (x, -y+2). This process should be repeated for each vertex of the triangle ABC to obtain all vertices of the triangle DEF.