Question

which order did becca perform the transformations? choose one option from each drop - down menu to answer the question. becca could have performed the transformations in either order. if she rotated triangle ( abc ) and then dilated it, the resulting triangle would be a different size than triangle ( abc ) on the coordinate grid. if she dilated triangle ( abc ) and then rotated it, the resulting triangle would be in a different location than triangle ( abc ) on the coordinate grid.

Explanation:

To solve this, we analyze the properties of rotations and dilations:

First Drop - Down (Order of Transformations)

Rotations (rigid transformations) preserve shape and size, while dilations (non - rigid, similarity transformation) change size. The key here is that the order of rotation and dilation can be swapped in some cases, but we also need to consider the effect on the final figure. However, from the context of the problem (the subsequent statements about size and location), we know that the order of rotation and dilation can be either order. So the first drop - down answer is "could have performed the transformations in either order".

Second Drop - Down (Rotate then Dilate)

A rotation doesn't change the size of the triangle. But a dilation changes the size of the figure. If we first rotate triangle \(ABC\) (size remains the same) and then dilate it, the resulting triangle will have a different size compared to triangle \(A''B''C''\) (assuming \(A''B''C''\) is the result of a different order of transformations, maybe dilate then rotate or some other combination where size is preserved in a way). So the second drop - down answer is "a different size than triangle \(A''B''C''\)".

Third Drop - Down (Dilate then Rotate)

A dilation changes the size of the triangle but not its shape (it's a similarity transformation). A rotation changes the position of the triangle. If we first dilate triangle \(ABC\) (changes size, keeps shape) and then rotate it, the resulting triangle will be in a different location on the coordinate grid compared to triangle \(A''B''C''\) (assuming \(A''B''C''\) is the result of a different order, like rotate then dilate, where the rotation's effect on position is combined with dilation in a different sequence). So the third drop - down answer is "in a different location than triangle \(A''B''C''\)".

Final Answers

1. First drop - down: could have performed the transformations in either order
2. Second drop - down: a different size than triangle \(A''B''C''\)
3. Third drop - down: in a different location than triangle \(A''B''C''\)

Answer:

To solve this, we analyze the properties of rotations and dilations:

First Drop - Down (Order of Transformations)

Rotations (rigid transformations) preserve shape and size, while dilations (non - rigid, similarity transformation) change size. The key here is that the order of rotation and dilation can be swapped in some cases, but we also need to consider the effect on the final figure. However, from the context of the problem (the subsequent statements about size and location), we know that the order of rotation and dilation can be either order. So the first drop - down answer is "could have performed the transformations in either order".

Second Drop - Down (Rotate then Dilate)

A rotation doesn't change the size of the triangle. But a dilation changes the size of the figure. If we first rotate triangle \(ABC\) (size remains the same) and then dilate it, the resulting triangle will have a different size compared to triangle \(A''B''C''\) (assuming \(A''B''C''\) is the result of a different order of transformations, maybe dilate then rotate or some other combination where size is preserved in a way). So the second drop - down answer is "a different size than triangle \(A''B''C''\)".

Third Drop - Down (Dilate then Rotate)

A dilation changes the size of the triangle but not its shape (it's a similarity transformation). A rotation changes the position of the triangle. If we first dilate triangle \(ABC\) (changes size, keeps shape) and then rotate it, the resulting triangle will be in a different location on the coordinate grid compared to triangle \(A''B''C''\) (assuming \(A''B''C''\) is the result of a different order, like rotate then dilate, where the rotation's effect on position is combined with dilation in a different sequence). So the third drop - down answer is "in a different location than triangle \(A''B''C''\)".

Final Answers

1. First drop - down: could have performed the transformations in either order
2. Second drop - down: a different size than triangle \(A''B''C''\)
3. Third drop - down: in a different location than triangle \(A''B''C''\)