To determine which transformation occurred from point \( Q(-3, -5) \) to point \( Q'(5, -3) \), we can analyze the coordinates.
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First, let's calculate the changes in the coordinates:
- Original point: \( Q(-3, -5) \)
- Transformed point: \( Q'(5, -3) \)
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To visualize the transformation, let's analyze the individual transformations:
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90-degree (counterclockwise) rotation: The rule is \( (x, y) \rightarrow (-y, x) \)
- Applying to \( Q(-3, -5) \):
- New coordinates: \( (5, -3) \) (this matches \( Q' \))
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90-degree (clockwise) rotation: The rule is \( (x, y) \rightarrow (y, -x) \)
- Applying to \( Q(-3, -5) \):
- New coordinates: \( (-5, 3) \) (not a match)
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180-degree rotation (clockwise or counterclockwise): The rule for both is \( (x, y) \rightarrow (-x, -y) \)
- Applying to \( Q(-3, -5) \):
- New coordinates: \( (3, 5) \) (not a match)
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270-degree (counterclockwise) rotation (which is the same as a 90-degree clockwise): The rule is equivalent and gives the same output as the 90-degree clockwise rotation, so it would also yield \( (-5, 3) \) (not a match).
Given that a \( 90 \)-degree counterclockwise rotation from point \( Q(-3, -5) \) properly leads to point \( Q'(5, -3) \), the transformation that occurred is:
a 90-degree (counterclockwise) rotation.