Chapter 1: Orienting Yourself: The Use of Coordinates

Exercise

Question

Question: 5

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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?

Answer

1
Think about which values can be used for the x- and y-coordinates if negative numbers are not available. Which parts of the coordinate plane could we then represent?
Coordinate plane with the first quadrant and non-negative parts of the axes highlighted in green, and the remaining three quadrants highlighted in red.
Coordinate plane showing the region highlighted in green that can be represented without negative numbers.
Answer: The coordinate system would have only non-negative values on both axes. Therefore, it would cover Quadrant I, along with the non-negative parts of the x- and y-axes.
2
Think about the points that lie to the left of the y-axis or below the x-axis. What happens to their coordinates if negative numbers are not available?
Answer: No, this system would not allow us to locate all the points on a 2-D plane.
Reason: A 2-D plane extends in all directions from the origin, so points can lie to the right, left, above, or below the origin.
Points to the left of the y-axis or below the x-axis need negative coordinates. Therefore, negative numbers are needed to represent points in Quadrants II, III, and IV.
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