Question

Tomas is planning a rail trail using a map with a marked grid. the head of the tail, which has a guide booth, is at (3,0). He moves 1 unit east and 3 units north and places a pin at (4,3) to mark the location guide booth. He continues to move 1 unit east and 3 units north twelve more times, placing a pin each time. where will the last pin be placed? Enter the coordinate in the boxes.



(___________,_____________)

Answer 1

To determine the location of the last pin placed by Tomas, we can analyze his movements in a systematic way.

Starting from the initial position:

- Head of the trail: (3, 0)
- Each movement consists of moving 1 unit east (which affects the x-coordinate) and 3 units north (which affects the y-coordinate).

Tomas performs the movement 12 more times after placing the first pin at (4, 3).

Each time he moves:
- The x-coordinate increases by 1.
- The y-coordinate increases by 3.

For 12 movements, the total changes in the coordinates will be:
- Change in x-coordinate: \( 12 \times 1 = 12 \)
- Change in y-coordinate: \( 12 \times 3 = 36 \)

Now let's compute the final coordinates after all movements:

Starting coordinates: (3, 0)

Final x-coordinate:
\[
3 + 12 = 15
\]

Final y-coordinate:
\[
0 + 36 = 36
\]

Thus, the coordinate where the last pin will be placed is:

(15, 36)

So the answer is:

(___________,_____________)
(15, 36)