What would a system of coordinates be like if we did not have negative numbers? Would this system allow us to locate all the points on a 2-D plane?
If we did not have negative numbers, a coordinate system would only consist of distances to the right of the origin and upwards from the origin. Since distances to the left and downwards are considered negative, we would not be able to mark these directions.
The axes would not divide the plane into four quadrants. Instead, the system would only represent the first quadrant, where both the - and -coordinates are positive.
No, this system would not allow us to locate all the points on a 2-D plane. We would be unable to locate any points that lie in Quadrants II, III, and IV, as locating points there requires negative - or -coordinates.
Explanation
The textbook explicitly states that distances to the right and upwards are positive, while distances to the left and downwards are negative. Without negative numbers, the coordinate axes could only extend in the positive directions, restricting the system entirely to Quadrant I (where both coordinates are positive). Points in the other three quadrants require at least one negative coordinate, making it impossible to locate them in such a restricted system.