The correct answer is d. Rotation counterclockwise 270° about the origin.
Reflection across the x-axis: This would flip the triangle across the x-axis, resulting in triangle A''B''C'', which is not the same as triangle A'B'C'.
Rotation 180° about the origin: This would rotate triangle ABC 180 degrees about the origin, resulting in triangle A''B''C', which is also not the same as triangle A'B'C'.
Translation 3 units down and 2 to the right: This would move triangle ABC 3 units down and 2 units to the right, resulting in triangle A''B''C', which is once again not the same as triangle A'B'C'.
Rotation counterclockwise 270° about the origin: This would rotate triangle ABC 270 degrees counterclockwise about the origin, resulting in triangle A'B'C'. This matches the triangle shown in the image.
Therefore, the only transformation that results in triangle A'B'C' is a rotation of 270 degrees counterclockwise about the origin.