The figure shows two triangles on a coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 4, 1 vertex B on ordered pair negative 3,1, and vertex C on ordered pair negative 4, 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair 4, 4, vertex B prime on ordered pair 3, 4, and vertex C prime on ordered pair 4,1.
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (5 points)
A. A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down
B. A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin
C. A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
D. A translation 5 units to the right, followed by a 270-degree counterclockwise rotation about the origin
The correct answer is D. A translation 5 units to the right, followed by a 270-degree counterclockwise rotation about the origin.
To form triangle A'B'C' from triangle ABC, you can observe that A' is obtained by translating A 5 units to the right, and B' is obtained by translating B 5 units to the right as well. Additionally, C' is obtained by rotating C 270 degrees counterclockwise about the origin.