The composition of rigid motions Upper T Subscript left angle negative 15 comma 3 right angleT−15,3circle◦Upper T Subscript left angle 21 comma negative 2 right angleT21,−2 describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive​ y-axis points north.

Question

Question content area bottom
Part 1
First the limousine drives enter your response here ​block(s)
▼
east
west
and enter your response here ​block(s)
▼
north,
south,
and then it drives enter your response here ​block(s)
▼
east
west
and enter your response here ​block(s)
▼
south.
north.

Answer 1

To describe the route taken by the limousine based on the given transformations, let's analyze the two transformations \( T_{(-15,3)} \) and \( T_{(21,-2)} \).

1. Starting Position: The limousine starts at the coordinates \( (-15, 3) \).

2. First Transformation: The move to \( (-15, 3) \) shows the limousine is beginning at these coordinates.

3. 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.