To determine the transformation that occurred from point Q (-3, -5) to its image Q' (5, -3), let's analyze the changes in the coordinates:
- Original Point Q: (-3, -5)
- Transformed Point Q': (5, -3)
We can look for patterns based on common transformations:
-
Reflection across the x-axis: Would change (-3, -5) to (-3, 5), which does not match.
-
Reflection across the y-axis: Would change (-3, -5) to (3, -5), which does not match.
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180-degree rotation: A 180-degree rotation around the origin takes (x, y) to (-x, -y). So:
- (Q) (-3, -5) would transform to (3, 5), which does not match.
-
90-degree counterclockwise rotation: Taking (x, y) to (-y, x):
- (-3, -5) would transform to (5, -3), which matches Q'.
-
270-degree counterclockwise rotation: Taking (x, y) to (y, -x):
- (-3, -5) would transform to (-5, 3), which does not match.
based on the analysis, the transformation that took place from point Q (-3, -5) to point Q' (5, -3) is a 90-degree counterclockwise rotation.