Tomas starts at the point (3, 0) and places a pin at (4, 3) after moving 1 unit east and 3 units north. He continues to place pins, moving 1 unit east and 3 units north from the most recently placed pin.
Let's find the coordinates of the pins Tomas will place:
- Starting point: (3, 0)
- First pin: (4, 3)
- Second pin: (5, 6) (from (4, 3) moving 1 unit east and 3 units north)
- Third pin: (6, 9) (from (5, 6) moving 1 unit east and 3 units north)
Continuing this, we can see that the coordinates of the pins are:
- After 0 moves: (3, 0)
- After 1 move: (4, 3)
- After 2 moves: (5, 6)
- After 3 moves: (6, 9)
- After 4 moves: (7, 12)
- After 5 moves: (8, 15)
The pattern shows that for each pin, the x-coordinate increases by 1, and the y-coordinate increases in increments of 3 (1st pin: y = 0 + 3, 2nd pin: y = 3 + 3 = 6, etc.).
From this pattern, the coordinates of the pins can be expressed as follows:
- Pin(n) = (3+n, 3n) for n = 0, 1, 2, 3...
So the points where pins will be placed include:
- (3, 0)
- (4, 3)
- (5, 6)
- (6, 9)
- (7, 12)
- (8, 15)
Thus, if the options include (3, 0), (4, 3), (5, 6), (6, 9), (7, 12), and (8, 15), you should select those points that correspond to the pins placed.
To summarize, the pins will be at the following coordinates:
- (3, 0)
- (4, 3)
- (5, 6)
- (6, 9)
- (7, 12)
- (8, 15)
If "6, 8" is not part of the pin placements, it follows the correct observation. Please let me know if you have other specific points to check!