Question

arranging a sports complex
a city is building a new sports complex. the initial plan and final plan of the layout of the sports context is shown. soccer field a was rotated and translated to the left in the final plan.
describe the transformations, if any, that each structure b - i went through between the initial and final plans.

Explanation:

Structure B

• Step1: Check for rotation
• In the initial plan, structure B is in a vertical orientation. In the final plan, it is also in a vertical orientation. So, no rotation.
• Step2: Check for translation
• In the initial plan, structure B is on the right - hand side. In the final plan, it is in the middle. So, it is translated to the left.

Structure C

• Step1: Check for rotation
• In the initial plan, structure C is in a horizontal orientation. In the final plan, it is in a vertical orientation. So, it is rotated \(90^{\circ}\) (assuming a counter - clockwise rotation, but the direction can be determined based on the coordinate system; here we just note the rotation).
• Step2: Check for translation
• In the initial plan, structure C is at the bottom - right. In the final plan, it is at the top - right. So, it is translated upwards.

Structures D and E

• Step1: Check for rotation
• Their orientations (rectangular shape with no change in side - to - side or top - to - bottom relations) remain the same. So, no rotation.
• Step2: Check for translation
• Their positions within the complex (relative to other structures) remain the same. So, no translation.

Structure F

• Step1: Check for rotation
• Its orientation (the shape of the baseball field) remains the same. So, no rotation.
• Step2: Check for translation
• In the initial plan, it is on the left - hand side (top). In the final plan, it is on the left - hand side (middle). So, it is translated downwards.

Structure G

• Step1: Check for rotation
• Its orientation (the shape of the baseball field) remains the same. So, no rotation.
• Step2: Check for translation
• In the initial plan, it is on the left - hand side (middle). In the final plan, it is on the right - hand side (middle). So, it is translated to the right.

Structure H

• Step1: Check for rotation
• Its orientation (the shape of the baseball field) remains the same. So, no rotation.
• Step2: Check for translation
• In the initial plan, it is on the left - hand side (lower - middle). In the final plan, it is on the left - hand side (lower). So, it is translated downwards.

Structure I

• Step1: Check for rotation
• Its orientation (the shape of the baseball field) remains the same. So, no rotation.
• Step2: Check for translation
• In the initial plan, it is on the left - hand side (bottom). In the final plan, it is on the right - hand side (bottom). So, it is translated to the right.

Answer:

• Structure B: Translated to the left.
• Structure C: Rotated (e.g., \(90^{\circ}\)) and translated upwards.
• Structures D and E: No transformation (no rotation or translation).
• Structure F: Translated downwards.
• Structure G: Translated to the right.
• Structure H: Translated downwards.
• Structure I: Translated to the right.