Question

1.)Can you map shape I onto shape II by a sequence of transformations? If so, give a sequence of transformations that maps shape I onto shape II.
2.)Complete the sequence of transformations you found in part A, but in a different order. Does this also map shape I onto shape II? What does this mean?

3.)If you reflect any shape across the x-axis and then rotate it 90° clockwise about the origin, do you get the same result as if you reflect it across the y-axis and then rotate it 90° counterclockwise about the origin? What does this mean?

4.)If you reflect any shape across the x-axis and then rotate it 180° about the origin, do you get the same result that you would if you reflect it across the y-axis and then rotate it 180° about the origin? What does that mean?

5.)If you reflect any shape across the x-axis and then across the y-axis, do you get the same result that you would if you rotated it 180° about the origin? What does that mean?

Answer 1

Answer:

1.) Yes, it is possible to map shape I onto shape II using a sequence of transformations. One sequence involves reflecting shape I across the x-axis, rotating it 90° counterclockwise about the origin, and translating the shape 8 units up and 4 units left.

2.) Make a conjecture regarding a single rotation that will map ABC to A″B″C″. ... Specify a sequence of transformations that will carry a given figure onto ... of transformations that will carry a given figure onto another. Also. G-CO.A.2, G-CO. B.6 ... performing the transformations in Part B in a different order. 6.

No, if the sequence of transformations changes, shape 1 does not map shape 2. This means that the order of the transformations has an effect on the final shape.

3.) Yes, reflecting a shape across the x-axis and then rotating it 90° clockwise about the origin gives the same results as reflecting it across the y-axis followed by rotating it 90° counterclockwise about the origin. This means these two sequences of transformations are equivalent.

4.) No, the finished shapes would be in different quadrants

5.)Yes, for a shape, reflections across x- and y-axes give the same result as a 180° rotation about the origin. That means these two sequences of transformations are equivalent.

Step-by-step explanation: