Tomas is planning a rail trail using a map with a marked grid. The head of the trail, 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 of another guide booth. He continues placing pins so that each pin is 1 unit east and 3 unit north of the previous pin. where is the fifth guide booth located?

Question

(5,5)
(5,10)
(7,12)
(8,15)

Answer 1

Tomas starts at the first guide booth at point (3, 0). He then places additional pins by moving 1 unit east and 3 units north for each subsequent booth.

Let's list the coordinates of the guide booths step-by-step:

1. First guide booth: (3, 0)
2. Second guide booth: Moves to (3 + 1, 0 + 3) = (4, 3)
3. Third guide booth: Moves to (4 + 1, 3 + 3) = (5, 6)
4. Fourth guide booth: Moves to (5 + 1, 6 + 3) = (6, 9)
5. Fifth guide booth: Moves to (6 + 1, 9 + 3) = (7, 12)

Therefore, the fifth guide booth is located at (7, 12).

The correct answer is (7,12).