Questions: Select all the correct answers. Which sequences of transformations confirm the congruence of shape II and shape I? a reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin a reflection of shape I across the x-axis followed by a 90° counterclockwise rotation about the origin a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin a reflection of shape I across the y-axis followed by a 90° clockwise rotation about the origin a reflection of shape I across the x-axis followed by a 180° rotation about the origin

Select all the correct answers.

Which sequences of transformations confirm the congruence of shape II and shape I? a reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin a reflection of shape I across the x-axis followed by a 90° counterclockwise rotation about the origin a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin a reflection of shape I across the y-axis followed by a 90° clockwise rotation about the origin a reflection of shape I across the x-axis followed by a 180° rotation about the origin

Transcript text: Select all the correct answers. Which sequences of transformations confirm the congruence of shape II and shape I? a reflection of shape I across the $x$-axis followed by a $90^{\circ}$ clockwise rotation about the origin a reflection of shape I across the $x$-axis followed by a $90^{\circ}$ counterclockwise rotation about the origin a reflection of shape I across the $y$-axis followed by a $90^{\circ}$ counterclockwise rotation about the origin a reflection of shape I across the $y$-axis followed by a $90^{\circ}$ clockwise rotation about the origin a reflection of shape I across the $x$-axis followed by a $180^{\circ}$ rotation about the origin

Solution

Solution Steps

Step 1: Analyze the transformations

Let's analyze each option:

Option 1: Reflecting shape I across the x-axis changes its coordinates from (x, y) to (x, -y). A 90° clockwise rotation about the origin changes the coordinates from (x, -y) to (-y, -x). This maps shape I to the same quadrant as shape II.
Option 2: Reflecting shape I across the x-axis changes its coordinates from (x, y) to (x, -y). A 90° counterclockwise rotation about the origin changes the coordinates from (x, -y) to (y, x). This maps shape I to a different quadrant than shape II.
Option 3: Reflecting shape I across the y-axis changes its coordinates from (x, y) to (-x, y). A 90° counterclockwise rotation about the origin changes the coordinates from (-x, y) to (-y, -x). This maps shape I to the same quadrant as shape II.
Option 4: Reflecting shape I across the y-axis changes its coordinates from (x, y) to (-x, y). A 90° clockwise rotation about the origin changes the coordinates from (-x, y) to (y, -x). This maps shape I to a different quadrant than shape II.
Option 5: Reflecting shape I across the x-axis changes its coordinates from (x, y) to (x, -y). A 180° rotation about the origin changes the coordinates from (x, -y) to (-x, y). This maps shape I to a different quadrant than shape II.

Step 2: Identify the correct transformations

By comparing the positions and orientations of shape I and shape II, we can see that options 1 and 3 result in the correct mapping.

Final Answer

A reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin, and a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin.

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