Question

Thomas is planning out a rail trail using a map with a marked grid the head of the trail which has an information kiosk it's located at (3, 0) He moves one unit east and three units north and places a pin at (4, 3) to represent the location of another information kiosk He continues to move one unit east and three units north 12 more times placing a pin each time where would the last pen be placed enter the coordinates in the boxes

Answer 1

Let's break down Thomas's movements step-by-step:

1. **Starting point**: (3, 0)
2. **First move**: he moves one unit east (increasing x by 1) and three units north (increasing y by 3).
- New coordinates after the first move:
\[
(3 + 1, 0 + 3) = (4, 3)
\]
3. **Continued movements**: He repeats this move (1 unit east and 3 units north) 12 more times.

Each of these moves changes his coordinates by adding (1, 3) to his current position.

The total number of moves, including the initial move:
- 1 (initial) + 12 (more moves) = 13 moves total.

So, the total change in coordinates from the starting point after 13 moves will be:
\[
(1 \times 13, 3 \times 13) = (13, 39)
\]

Now, we can find the coordinates of the last pin by adding this change to the initial coordinates:
\[
(3, 0) + (13, 39) = (3 + 13, 0 + 39) = (16, 39)
\]

Thus, the coordinates of the last pin would be **(16, 39)**.