Question

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 point) Responses rotation, then translation rotation, then translation rotation, then reflection rotation, then reflection translation, then rotation translation, then rotation reflection, then translation

Answer 1

To move a triangle in Quadrant IV to a triangle in Quadrant II and show that they are congruent, we can perform the following series of transformations:

1. Rotation: Rotate the triangle 180 degrees around the origin. This will move the triangle from Quadrant IV to Quadrant II because a rotation of 180 degrees will map points in Quadrant IV to their respective points in Quadrant II.

2. Translation: If needed, you can then translate the triangle to match the exact position of the triangle in Quadrant II.

This series of transformations (rotation followed by translation) will effectively show that the triangles are indeed congruent, since a rotation does not change the size or shape of the triangle, and translation merely shifts it to a different location without altering its dimensions.

Therefore, the response that describes this transformation is rotation, then translation.