To describe the route taken by the limousine based on the given transformations, let's analyze the two transformations \( T_{(-15,3)} \) and \( T_{(21,-2)} \).
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Starting Position: The limousine starts at the coordinates \( (-15, 3) \).
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First Transformation: The move to \( (-15, 3) \) shows the limousine is beginning at these coordinates.
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Second Transformation: The new position after the second transformation is \( (21, -2) \).
Now, let's calculate the movement in the x-direction (east-west) and y-direction (north-south):
X-axis Movement:
- Starting x-coordinate: \(-15\)
- Ending x-coordinate: \(21\)
- Movement in the x-direction: \( 21 - (-15) = 21 + 15 = 36\)
- Since the movement is positive, the limousine moves east.
Y-axis Movement:
- Starting y-coordinate: \(3\)
- Ending y-coordinate: \(-2\)
- Movement in the y-direction: \(-2 - 3 = -5\)
- Since the movement is negative, the limousine moves south.
Summary of the Route:
- The limousine drives 36 block(s) east,
- then it drives 5 block(s) south.
Final Text Describing the Route:
The limousine drives 36 block(s) east and 5 block(s) south.