To determine the function mapping and degree of rotation used to map triangle PQR to triangle P'Q'R', we can start by examining the coordinates of the points before and after the transformation:
- Point P(2, -5) maps to P'(-2, 5)
- Point Q(0, -3) maps to Q'(0, 3)
- Point R(7, 1) maps to R'(-7, -1)
Let's analyze how the points change.
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For point P(2, -5) to P'(-2, 5):
- The x-coordinate changes from 2 to -2 (which is equivalent to multiplying by -1).
- The y-coordinate changes from -5 to 5 (which is also equivalent to multiplying by -1).
This transformation can be expressed as: \[ (x, y) \to (-x, -y) \]
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For point Q(0, -3) to Q'(0, 3):
- The x-coordinate remains the same (0).
- The y-coordinate changes from -3 to 3 (which is equivalent to multiplying by -1).
This confirms the transformation: \[ (0, -3) \to (0, -(-3)) \to (0, 3) \]
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For point R(7, 1) to R'(-7, -1):
- The x-coordinate changes from 7 to -7 (which is equivalent to multiplying by -1).
- The y-coordinate changes from 1 to -1 (which is also equivalent to multiplying by -1).
Again, this confirms the transformation: \[ (7, 1) \to (-7, -1) \]
Based on the analysis, we can conclude that the function mapping that transforms triangle PQR to triangle P'Q'R' is: \[ (x, y) \to (-x, -y) \]
Now, regarding the degree of rotation, the transformation \( (x, y) \to (-x, -y) \) corresponds to a 180-degree rotation around the origin.
Conclusion
The function mapping used is: \[ (x,y) \to (-x, -y) \] And the degree of rotation is: \[ 180 \text{ degrees} \]