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

1) Yes, we can map shape I onto shape II by a sequence of transformations. A possible sequence of transformations is: Translation, Reflection, and Rotation. 2) Completing the sequence of transformations in a different order may or may not map shape I onto shape II. 3) The order in which you perform reflections and rotations affects the final result and the resulting shapes will be different.

Step-by-step explanation:

1) Yes, we can map shape I onto shape II by a sequence of transformations. A possible sequence of transformations is:

• Translation: Shift shape I to the left by 2 units
• Reflection: Reflect shape I across the x-axis
• Rotation: Rotate shape I 90° clockwise about the origin

2) Completing the sequence of transformations in a different order may or may not map shape I onto shape II. This depends on the specific transformations used. If the new sequence of transformations still involves the same types of transformations (translation, reflection, and rotation), but in a different order, then it will map shape I onto shape II. If different types of transformations are used or if the order of transformations fundamentally changes, then it may not map shape I onto shape II.

3) If you reflect any shape across the x-axis and then rotate it 90° clockwise about the origin, you do not get the same result as if you reflect it across the y-axis and then rotate it 90° counterclockwise about the origin. This means that the order in which you perform reflections and rotations affects the final result, and the resulting shapes will be different.

4) If you reflect any shape across the x-axis and then rotate it 180° about the origin, you do get the same result that you would if you reflect it across the y-axis and then rotate it 180° about the origin. This means that both sequences of transformations produce the same final shape.

5) If you reflect any shape across the x-axis and then across the y-axis, you do get the same result that you would if you rotated it 180° about the origin. This means that reflection across both the x-axis and y-axis is equivalent to a 180° rotation about the origin.

Answer 2

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: