Compositions of Transformations Quick Check 3 of 53 of 5 Items Question Use the image to answer the question. Determine the congruence transformation used on △ABC that resulted in △DEF . (1 point) Responses △ABC was rotated −180° (clockwise) or 180° (counterclockwise), then shifted 2 units to the right and 2 units up. triangle upper A upper B upper C was rotated negative 180 degrees (clockwise) or 180 degrees (counterclockwise), then shifted 2 units to the right and 2 units up. △ABC was shifted 2 units to the left and 2 units up, then reflected across the y-axis. triangle upper A upper B upper C was shifted 2 units to the left and 2 units up, then reflected across the y -axis. △ABC was shifted 2 units to the right and 2 units up, then rotated 180° (counterclockwise). triangle upper A upper B upper C was shifted 2 units to the right and 2 units up, then rotated 180 degrees (counterclockwise). △ABC was reflected across the y-axis, then shifted 2 units to the right and 2 units up. triangle upper A upper B upper C was reflected across the y -axis, then shifted 2 units to the right and 2 units up. Skip to navigation page 14 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the congruence transformation used on triangle \( \triangle ABC \) to result in triangle \( \triangle DEF \), you would generally analyze the position and orientation of the two triangles in the image provided. However, since I cannot see the image, I can guide you through the reasoning process to find the correct transformation.

1. Check for Rotation: Determine if triangle \( \triangle ABC \) has been rotated to align with triangle \( \triangle DEF \). A rotation of 180° (either direction) would flip the triangle; you would check if points \( A, B, \) and \( C \)’s locations relative to the origin line up with \( D, E, \) and \( F \).

2. Check for Translation: After checking for any possible rotations, see if there has been a translation. This could involve moving the triangle left, right, up, or down.

3. Check for Reflection: Determine if triangle \( \triangle ABC \) has been reflected over any line (for example, the y-axis). If so, you can see how these points land relative to the original.

4. Combine Transformations: If multiple transformations are involved (like rotation followed by translation), apply the transformations sequentially to check for the match to triangle \( \triangle DEF \).

Given these routes of analysis, narrow down which option correctly describes the series of transformations from \( \triangle ABC \) to \( \triangle DEF \).

If you can provide more information about the positions of triangles \( ABC \) and \( DEF \) or share specific coordinates, I can help verify the transformations more accurately.