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Sep10

Cartesian Coordinates: The Quadrants

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In an earlier post we discovered what coordinates are and what they are used for. Today we are going to look into this topic a little more to get to know this system better.

What is a quadrant on the Cartesian coordinate axis?

In the two dimensional Cartesian coordinate system, the 2 axes (X and Y) intersect at the origin (O)  and divide the coordinate plane into 4 regions:

Coordinates

These regions are called quadrants. They are numbered from 1 to 4, with Roman numerals, counter clockwise,  around a central point of origin.

Coordinates

First Quadrant

Until now, we only knew the origin O and the first quadrant. In it, the coordinates X and Y are always positive numbers.

  • X positive means that the position is to the right of the origin.
  • Y positive means that it is above the origin.

So, in this quadrant, (X,Y) are positive. We can write them abbreviated as (+,+).

Coordinates

The yellow dot is on the coordinates (3,3). Three positions to the right of the origin and three above.

Second Quadrant

The first negative coordinate appears in this quadrant. The positive values tell us how many positions to count to the right or above the origin, X and Y respectively. In the same way, the negative values indicate how many positions we count to the left or below the origin of the X and Y axes. For example, if the X coordinate has a value of (-5) it means that it is 5 positions to the left of the origin. If the Y coordinate has the value of (-1), it means that it is one position below the origin.

  • X negative indicates that the position is to the left of the origin.
  • Y positive that it is above the origin.

Thus (X,Y) are written (-,+).

Coordinates

In the example, the green dot is on the coordinates (-3,1). Three positions to the left of the origin and one position above.

Third Quadrant

Here, both values are negative.

  • X negative indicates that the position is to the left of the origin.
  • Y negative that it is below the origin.

Therefore (X,Y) are written (-,-).

Coordinates

The red point is on the coordinates (-2,-5). Two positions to the left of the origin and five positions below.

Fourth Quadrant

The last quadrant is to the right and below the origin. The values of X and Y will be positive and negative respectively.

  • X positive indicates that the position is to the right of the origin.
  • Y negative that it is below the origin.

In other words (X,Y) are written (+,-).

Coordinates

The blue dot is on the coordinates (4,-4). Four positions to the right of the origin and four below.

Summary

To summarize, the positive or negative value of the X and Y coordinates indicate their relative position with respect to the origin:

  • On the X axis, horizontal direction, a positive value reflects a position to the right of the origin. And a negative, to the left.
  • On the Y axis, vertical direction, the positive value indicates a position above the origin while a negative value indicates one below.
  • If X has a value of zero, the position of the coordinate is not to the right or left of the origin. It would be at some point on the Y axis.
  • If Y has a value of zero, the position of the coordinate is not above or below the origin. It would be at some point on the X axis.
  • O, the origin, is the only position in which both values are zero.

In conclusion, knowing the values of (X,Y) we can know which quadrant that position is in according to the following framework:

Coordinates

If you want to practice and learn more about the coordinates, and other primary mathematics topics, go to Smartick and try it for free.

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