you start a search for a buried object by marking the center of the field as (0,0), with coordinates giving distances in yards. Coordinates to the north or east are positive, and coordinates to the south or west are negative. You find nothing at (-5,3), so you try a likely looking spot 6 yards to the east and 5 yards to the south of the first spot. What are the coordinates of the second spot?
The coordinates of the second spot are (1,-2).
Starting from the first spot at (-5,3), moving 6 yards to the east means adding 6 to the x-coordinate, giving (-5+6, 3) or (1,3). Then, moving 5 yards to the south means subtracting 5 from the y-coordinate, giving (1, 3-5) or (1,-2).
To find the coordinates of the second spot, we can start with the coordinates of the first spot (-5,3) and add the respective distances.
The first spot is -5 yards to the west and 3 yards to the north of the center (0,0).
To get to the second spot, we move 6 yards to the east and 5 yards to the south of the first spot.
Adding 6 yards to the east to the x-coordinate (-5 + 6) gives us -5 + 6 = 1.
Adding 5 yards to the south to the y-coordinate (3 - 5) gives us 3 - 5 = -2.
Therefore, the coordinates of the second spot are (1, -2).