Question
It looks like the attached image displays triangles on a coordinate plane, but it doesn't seem to match your original question about finding a line of reflection for a quadrilateral. Could you clarify or reattach the diagram you’re referring to? I’d be happy to help you solve the problem for quadrilateral PQRS!
△ABC
was transformed into △DEF
. Determine which statement about this transformation is correct.
Statement #1: △ABC≅△DEF
because △ABC
was shifted 2 units to the left and 3 units down, then reflected across the y-axis.
Statement #2: △ABC≅△DEF
because △ABC
was shifted 2 units to the right and 3 units down, then rotated 180°
(counterclockwise).
Statement #3: △ABC≅△DEF
because △ABC
was shifted 2 units to the right and 3 units down, then rotated −270°
(clockwise).
(1 point)
Statement #
is correct.
△ABC
was transformed into △DEF
. Determine which statement about this transformation is correct.
Statement #1: △ABC≅△DEF
because △ABC
was shifted 2 units to the left and 3 units down, then reflected across the y-axis.
Statement #2: △ABC≅△DEF
because △ABC
was shifted 2 units to the right and 3 units down, then rotated 180°
(counterclockwise).
Statement #3: △ABC≅△DEF
because △ABC
was shifted 2 units to the right and 3 units down, then rotated −270°
(clockwise).
(1 point)
Statement #
is correct.
Answers
GPT-4o mini
To determine which statement about the transformations from triangle \( \triangle ABC \) to triangle \( \triangle DEF \) is correct, we need to consider the properties of congruence and the nature of the transformations mentioned in each statement.
1. **Statement #1**: Claims that \( \triangle ABC \) was shifted 2 units to the left and 3 units down, then reflected across the y-axis.
- A shift (translation) followed by a reflection should still result in triangles that are congruent, provided that the total transformation preserves distances and angles. If this transformation was indeed applied correctly and the coordinates of \( \triangle DEF \) match those of \( \triangle ABC \) after this process, then this statement can be true. However, the specific movement (left instead of right) should be confirmed by the coordinates.
2. **Statement #2**: Claims that \( \triangle ABC \) was shifted 2 units to the right and 3 units down, then rotated 180° counterclockwise.
- A translation followed by a 180° rotation also preserves congruence. If this transformation results in the properties of \( \triangle DEF \) matching those of \( \triangle ABC \), this statement can be true. Again, we'd need to verify with the coordinates.
3. **Statement #3**: Claims that \( \triangle ABC \) was shifted 2 units to the right and 3 units down, then rotated -270° (clockwise).
- A clockwise rotation of 270° is equivalent to a counterclockwise rotation of 90°, meaning that the transformation is a type of rotation but needs to retain congruence properties. If following this transformation results in \( \triangle DEF \) being congruent to \( \triangle ABC \), then this statement can also be true.
Without specific coordinates or measurements, we cannot definitively say which statement is true. However, if you have a specific transformation that matches the change in coordinates between triangles \( ABC \) and \( DEF \), it would clarify which of the statements is indeed correct.
To conclude, ideally, you would check the actual coordinates after performing each transformation stated in the options to confirm which one leads to \( \triangle DEF \) being congruent to \( \triangle ABC \).
1. **Statement #1**: Claims that \( \triangle ABC \) was shifted 2 units to the left and 3 units down, then reflected across the y-axis.
- A shift (translation) followed by a reflection should still result in triangles that are congruent, provided that the total transformation preserves distances and angles. If this transformation was indeed applied correctly and the coordinates of \( \triangle DEF \) match those of \( \triangle ABC \) after this process, then this statement can be true. However, the specific movement (left instead of right) should be confirmed by the coordinates.
2. **Statement #2**: Claims that \( \triangle ABC \) was shifted 2 units to the right and 3 units down, then rotated 180° counterclockwise.
- A translation followed by a 180° rotation also preserves congruence. If this transformation results in the properties of \( \triangle DEF \) matching those of \( \triangle ABC \), this statement can be true. Again, we'd need to verify with the coordinates.
3. **Statement #3**: Claims that \( \triangle ABC \) was shifted 2 units to the right and 3 units down, then rotated -270° (clockwise).
- A clockwise rotation of 270° is equivalent to a counterclockwise rotation of 90°, meaning that the transformation is a type of rotation but needs to retain congruence properties. If following this transformation results in \( \triangle DEF \) being congruent to \( \triangle ABC \), then this statement can also be true.
Without specific coordinates or measurements, we cannot definitively say which statement is true. However, if you have a specific transformation that matches the change in coordinates between triangles \( ABC \) and \( DEF \), it would clarify which of the statements is indeed correct.
To conclude, ideally, you would check the actual coordinates after performing each transformation stated in the options to confirm which one leads to \( \triangle DEF \) being congruent to \( \triangle ABC \).