Describe the series of transformations that have occurred to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent.
1.translation, then rotation
2.reflection, then translation
3.rotation, then translation
4.rotation, then reflection
The correct answer is option 3: rotation, then translation.
To move the triangle in Quadrant IV to the triangle in Quadrant II, we can first perform a rotation about the origin to align the two triangles. This rotation can be counterclockwise or clockwise, depending on the specific angle of rotation.
After the rotation, the triangles will have the same orientation and size. However, they will not be in the same position. Therefore, a translation is needed to move the rotated triangle to coincide with the original triangle in Quadrant II.
Hence, the correct series of transformations is rotation, then translation.