2. You start a search for a buried object by marking the center of a 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 (−12, 8), so you try a likely- looking spot 3 yards to the east and 11 yards to the south of the first spot. What are the coordinates of the second spot? (1 point)
The coordinates of the second spot are (−9, −3).
Starting at the center of the field at (0,0), moving 3 yards to the east takes us to (3,0) and then moving 11 yards to the south from there takes us to (3,-11). However, we are marking our coordinates with respect to the starting point, so we need to subtract the eastward distance of 3 yards from the x-coordinate and the southward distance of 11 yards from the y-coordinate of (3,-11). This gives us (-9,-3) as the coordinates of the second spot relative to the center of the field.