Respuesta :
4.Rotate 120 degrees counterclockwise around center C , then rotate 220 degrees counterclockwise around C again
Step-by-step explanation:
We have the following statements:
1.Translate 3 units up, then 3 units down.
Translating a graph 3 units up , and then 3 units down will counter cancel each other . Original position returned here!
2.Reflect over line p , then reflect over line p again.
Reflecting over line p , and then again reflecting over p , counter cancelling each other . Original position returned here!
3.Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.
Translating 1 unit right and 4 units left i.e. move 3 left units then 3 units right which counter cancel each other . Original position returned here!
4.Rotate 120 degrees counterclockwise around center C , then rotate 220 degrees counterclockwise around C again
Rotating 120 degrees counterclockwise around center C , then rotating 220 degrees counterclockwise around C again will let it differ from 340 degrees from original position . Here , these sequences of transformations would not return a shape to its original position.
Transformation involves changing the position of a shape.
The transformation that would not return a shape to its original position is:
- Rotate [tex]120^o[/tex] counterclockwise around center C,
- Rotate [tex]220^o[/tex]counterclockwise around C again
(a) Translate 3 units up, then 3 units down
- Up and down translations are direct opposite translations.
- An upward movement by 3 units would be cancelled by a downward movement of 3 units, and the shape will return to its original position
(b) Reflect over line p, twice
- Reflections over the same line in an even-number times will cancel out each other.
- A reflection over line p twice, will return the shape to its initial position
(c) Translate 1 unit right, 4 units left and 3 units right
- Right and left translations are direct opposite translations.
We have:
[tex]Left = 4[/tex]
[tex]Right = 1 + 3 = 4[/tex]
- A 4 units movement in the right direction would be cancelled by a 4 units movement in the left direction
- The shape will return to its original position
(d) Rotate [tex]120^o[/tex] counterclockwise around center C, then rotate [tex]220^o[/tex]counterclockwise around C again
The first rotation is given as:
[tex]\theta_1 = 120^o[/tex] -- counterclockwise
The second rotation is given as:
[tex]\theta_2 = 220^o[/tex] -- counterclockwise
The total rotation is calculated as:
[tex]\theta = \theta_1 +\theta_2[/tex]
[tex]\theta = 120^o + 220^o[/tex]
[tex]\theta = 340^o[/tex]
This means that the shape is rotated [tex]340^o[/tex] counterclockwise.
For the shape to return to its original location, it must be rotated [tex]360^o[/tex] counterclockwise.
Hence, option (d) is correct
Read more about transformations at:
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