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Choose all sequences of transformations that produce the same image of a given figure.
a reflection across the y-axis followed by a clockwise rotation 90° about the origin
a reflection across the y-axis followed by a counter-clockwise rotation 90° about the origin
a clockwise rotation 90° about the origin followed by a reflection across the x-axis
a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis
a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin

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sqdancefan

All of these transformations are equivalent to reflection across the line y=x:

  • a reflection across the y-axis followed by a clockwise rotation 90° about the origin
  • a clockwise rotation 90° about the origin followed by a reflection across the x-axis
  • a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis
  • a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin

_____

These are all but the second choice.

... reflection across y: (x, y) ⇒ (-x, y); 90°CW: (-x, y) ⇒ (y, x)

... 90°CW: (x, y) ⇒ (y, -x); reflection across x: (y, -x) ⇒ (y, x)

... 90°CCW: (x, y) ⇒ (-y, x); reflection across y: (-y, x) ⇒ (y, x)

... reflection across x: (x, y) ⇒ (x, -y); 90°CCW: (x, -y) ⇒ (y, x)

Note that the second choice gives a different result:

... reflection across y: (x, y) ⇒ (-x, y); 90°CCW: (-x, y) ⇒ (-y, -x)

MrRoyal

Transformation involves changing the position and/or size of a figure.

None of the sequence of transformation not produce the same image

(a) Reflection across the y-axis, then a 90 degrees clockwise rotation

The rule of reflection across the y-axis is:

[tex]\mathbf{(x,y) \to (-x,y)}[/tex]

The rule of 90 degrees clockwise rotation is:

[tex]\mathbf{ (x, y) \to (y, -x)}[/tex]

So, we have:

[tex]\mathbf{ (-x, y) \to (y, x)}[/tex]

(x, y) and (y, x) are different.

Hence, this sequence of transformation does not produce the same image

(b) Reflection across the y-axis, then a 90 degrees counter-clockwise rotation

The rule of reflection across the y-axis is:

[tex]\mathbf{(x,y) \to (-x,y)}[/tex]

The rule of 90 degrees counter-clockwise rotation is:

[tex]\mathbf{ (x, y) \to (-y, x)}[/tex]

So, we have:

[tex]\mathbf{ (-x, y) \to (-y, -x)}[/tex]

(x, y) and (-y, -x) are different.

Hence, this sequence of transformation does not produce the same image

(c) A 90 degrees clockwise rotation, then a reflection across the x-axis

The rule of 90 degrees clockwise rotation is:

[tex]\mathbf{ (x, y) \to (y, -x)}[/tex]

The rule of reflection across the x-axis is:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

So, we have:

[tex]\mathbf{ (y, -x) \to (y, x)}[/tex]

(x, y) and (y, x) are different.

Hence, this sequence of transformation does not produce the same image

(d) A 90 degrees counter-clockwise rotation, then a reflection across the y-axis

The rule of 90 degrees counter-clockwise rotation is:

[tex]\mathbf{ (x, y) \to (-y, x)}[/tex]

The rule of reflection across the y-axis is:

[tex]\mathbf{(x,y) \to (-x,y)}[/tex]

So, we have:

[tex]\mathbf{ (-y, x) \to (y, x)}[/tex]

(x, y) and (y, x) are different.

Hence, this sequence of transformation does not produce the same image

(e) A reflection across the x-axis, then a counter-clockwise rotation 90 degrees

The rule of reflection across the x-axis is:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

The rule of 90 degrees counter-clockwise rotation is:

[tex]\mathbf{ (x, y) \to (-y, x)}[/tex]

So, we have:

[tex]\mathbf{ (x,-y) \to (y, x)}[/tex]

(x, y) and (y, x) are different.

Hence, this sequence of transformation does not produce the same image

Hence, none of the sequence of transformation not produce the same image

Read more about sequence of transformation at:

https://brainly.com/question/25210048

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