Final answer:
The correct answer is option d) None of the above.The combined transformations of translating along the vector (7,1) and reflecting across the x-axis result in new vertices which do not match any of the provided options.
Step-by-step explanation:
To solve this problem, we need to perform two transformations on each vertex of triangle EFG: a translation along the vector (7,1) and a reflection across the x-axis. For each vertex, add the translation vector to the original coordinates and then reflect the y-coordinate to get the new position of each vertex after the transformations.
- For vertex E(1,5), the translation gives us E'(1+7, 5+1) or E'(8,6). Reflecting across the x-axis gives us E''(8,-6).
- For vertex F(0,-3), the translation gives us F'(0+7, -3+1) or F'(7,-2). Reflecting across the x-axis gives us F''(7,2).
- For vertex G(-1,2), the translation gives us G'(-1+7, 2+1) or G'(6,3). Reflecting across the x-axis gives us G''(6,-3).
Therefore, none of the listed options a, b, or c are correct since none match the resulting coordinates after performing the combined translation and reflection.