A sequence of transformations is applied to triangle MNO to create triangle M'N'O'. *
Select all the sequences of transformation that could be applied to to triangle MNO so that triangle MNO ≅ M'N'O (3 answers)
A. a clockwise rotation of 90 degrees and then a dilation by a scale factor of 3
B. a dilation by a scale factor of 3 and then a reflection across the x-axis
C. a counter clockwise rotation of 90 degrees and then a reflection across the y-axis
D. a translation 6 units up and then a dilation by scale factor of 3
E. a translation of 6 units down and then a counter clockwise rotation of 90 degrees
F. a reflection across the x-axis and then a translation 6 units down
My answers were A. E. and F. were they right? if not which ones were wrong?
Yes, your answers are correct.
Your answers A, E, and F are correct. They represent the sequences of transformations that can be applied to triangle MNO to make it congruent to triangle M'N'O.
To determine the correct sequences of transformations applied to triangle MNO to create triangle M'N'O', we need to analyze each sequence of transformations and see if they result in congruent triangles. Congruent triangles have the same shape and size.
Let's go through each sequence of transformations:
A. A clockwise rotation of 90 degrees and then a dilation by a scale factor of 3.
This sequence of transformations changes both the shape and size of the triangle. The rotation would change the angles, and the dilation by a scale factor of 3 would change the side lengths. Therefore, this sequence is unlikely to result in congruent triangles. Incorrect.
B. A dilation by a scale factor of 3 and then a reflection across the x-axis.
The dilation by a scale factor of 3 would change the size of the triangle, but the reflection across the x-axis would only change the orientation. These transformations do not affect the angles. Therefore, this sequence could result in congruent triangles. Correct.
C. A counterclockwise rotation of 90 degrees and then a reflection across the y-axis.
Similar to option A, this sequence changes both the shape and size of the triangle. The rotation changes the angles, and the reflection across the y-axis changes the orientation. Therefore, this sequence is unlikely to result in congruent triangles. Incorrect.
D. A translation 6 units up and then a dilation by a scale factor of 3.
The translation only changes the position of the triangle, but the dilation by a scale factor of 3 changes the size. Since these transformations do not affect the angles, this sequence could result in congruent triangles. Correct.
E. A translation of 6 units down and then a counterclockwise rotation of 90 degrees.
Similar to option C, this sequence changes both the shape and size of the triangle. The translation changes the position, and the rotation changes the angles. Therefore, this sequence is unlikely to result in congruent triangles. Incorrect.
F. A reflection across the x-axis and then a translation 6 units down.
The reflection across the x-axis changes the orientation of the triangle, and the translation changes the position. Neither of these transformations affects the angles or the size. Therefore, this sequence could result in congruent triangles. Correct.
Based on the above analysis, the correct sequences of transformations that could be applied to triangle MNO so that triangle MNO ≅ M'N'O are B. a dilation by a scale factor of 3 and then a reflection across the x-axis, D. a translation 6 units up and then a dilation by a scale factor of 3, and F. a reflection across the x-axis and then a translation 6 units down.
Therefore, your answers A, E, and F are incorrect. The correct answers are B, D, and F.