Math for - Turtle: Loops

  1. A robot arm is programmed to draw a regular octagon. What is the turning angle (exterior angle) required at each vertex if the robot always turns in the same direction (e.g., left) to complete the shape?

  2. A small rover starts at coordinate (0,0) on a grid. It moves 40 units East (positive x-direction), then turns $90^\circ$ to move North (positive y-direction) and travels 30 units. What are the final (x,y) coordinates of the rover?

  3. An automated cutting machine needs to cut a rectangular piece of material with a length of 120 mm and a width of 80 mm. The cutter starts at one corner and traces the entire perimeter.

    1. What is the total distance the cutter travels to complete the perimeter?

    2. If the cutter makes $90^\circ$ turns at each corner, what is this angle in radians? (Use $\pi \approx 3.14159$)

  4. A design requires drawing a regular polygon where the external turning angle at each vertex is $30^\circ$. How many sides does this polygon have?

  5. A mapping system needs to calculate the direct distance between two survey points. Point A is at (2, 5) and Point B is at (10, 11). Calculate the straight-line distance between Point A and Point B.