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We can summarize sign patterns of the quadrants as follows. Also see [link] .

Quadrant I Quadrant II Quadrant III Quadrant IV
( x , y ) ( x , y ) ( x , y ) ( x , y )
(+,+) (−,+) (−,−) (+,−)
The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled “I” and “ordered pair +, +”, the top-left portion of the plane is labeled “II” and “ordered pair -, +”, the bottom-left portion of the plane is labelled “III”  “ordered pair -, -” and the bottom-right portion of the plane is labeled “IV” and “ordered pair +, -”.

What if one coordinate is zero? Where is the point ( 0 , 4 ) located? Where is the point ( −2 , 0 ) located? The point ( 0 , 4 ) is on the y -axis and the point ( 2 , 0 ) is on the x -axis.

Points on the axes

Points with a y -coordinate equal to 0 are on the x -axis , and have coordinates ( a , 0 ) .

Points with an x -coordinate equal to 0 are on the y -axis , and have coordinates ( 0 , b ) .

What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is ( 0 , 0 ) . The point has a special name. It is called the origin .

The origin

The point ( 0 , 0 ) is called the origin . It is the point where the x -axis and y -axis intersect.

Plot each point on a coordinate grid:

  1. ( 0 , 5 )
  2. ( 4 , 0 )
  3. ( −3 , 0 )
  4. ( 0 , 0 )
  5. ( 0 , −1 )

Solution

  1. Since x = 0 , the point whose coordinates are ( 0 , 5 ) is on the y -axis .
  2. Since y = 0 , the point whose coordinates are ( 4 , 0 ) is on the x -axis .
  3. Since y = 0 , the point whose coordinates are ( −3 , 0 ) is on the x -axis .
  4. Since x = 0 and y = 0 , the point whose coordinates are ( 0 , 0 ) is the origin.
  5. Since x = 0 , the point whose coordinates are ( 0 , −1 ) is on the y -axis . The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 0, 0” is labeled “0, 0” in parentheses. The point “ordered pair 4, 0” is labeled “4, 0” in parentheses. The point “ordered pair 0, 5” is labeled “0, 5” in parentheses. The point “ordered pair 0, -1” is labeled “ 0, -1” in parentheses.
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Plot each point on a coordinate grid:

  1. ( 4 , 0 )
  2. ( −2 , 0 )
  3. ( 0 , 0 )
  4. ( 0 , 2 )
  5. ( 0 , −3 )


This image is an answer graph and  shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The  point for ordered pair 4, 0 is plotted.  The point for ordered pair -2, 0 is plotted. The point for ordered pair 0,0 is plotted. The point for ordered pair 0, 2 is plotted. The point for ordered pair 0,-3 is plotted.

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Plot each point on a coordinate grid:

  1. ( −5 , 0 )
  2. ( 3 , 0 )
  3. ( 0 , 0 )
  4. ( 0 , −1 )
  5. ( 0 , 4 )


This image is an answer graph and  shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The  point for ordered pair -5, 0 is plotted.  The point for ordered pair 3, 0 is plotted. The point for ordered pair 0,0 is plotted. The point for ordered pair 0, -1 is plotted. The point for ordered pair 0,4 is plotted.

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Identify points on a graph

In algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the x -coordinate of a point on a graph, read the number on the x -axis    directly above or below the point. To identify the y -coordinate of a point, read the number on the y -axis    directly to the left or right of the point. Remember, to write the ordered pair using the correct order ( x , y ) .

Name the ordered pair of each point shown:

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 2, 4” is labeled C. The point “ordered pair -3, 3” is labeled A.  The point “ordered pair -1, -3” is labeled B. The point “ordered pair 4, -4” is labeled D.

Solution

Point A is above −3 on the x -axis , so the x -coordinate of the point is −3 . The point is to the left of 3 on the y -axis , so the y -coordinate of the point is 3 . The coordinates of the point are ( −3 , 3 ) .

Point B is below −1 on the x -axis , so the x -coordinate of the point is −1 . The point is to the left of −3 on the y -axis , so the y -coordinate of the point is −3 . The coordinates of the point are ( −1 , −3 ) .

Point C is above 2 on the x -axis , so the x -coordinate of the point is 2 . The point is to the right of 4 on the y -axis , so the y -coordinate of the point is 4 . The coordinates of the point are ( 2 , 4 ) .

Point D is below 4 on the x - axis , so the x -coordinate of the point is 4 . The point is to the right of −4 on the y -axis , so the y -coordinate of the point is −4 . The coordinates of the point are ( 4 , −4 ) .

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Name the ordered pair of each point shown:

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 5, 1” is labeled A. The point “ordered pair -2, 4” is labeled B.  The point “ordered pair -5, -1” is labeled C. The point “ordered pair 3, -2” is labeled D.

  1. A: (5,1)
  2. B: (−2,4)
  3. C: (−5,−1)
  4. D: (3,−2)

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Name the ordered pair of each point shown:

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 4, 2” is labeled A. The point “ordered pair -2, 3” is labeled B.  The point “ordered pair -4, -4” is labeled C. The point “ordered pair 3, -5” is labeled D.

  1. A: (4,2)
  2. B: (−2,3)
  3. C: (−4,−4)
  4. D: (3,−5)

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Name the ordered pair of each point shown:

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 3, 0” is labeled C. The point “ordered pair 0, 1” is labeled D.  The point “ordered pair -4, 0” is labeled A. The point “ordered pair 0, -2” is labeled B.

Solution

  1. Point A is on the x -axis at x = 4 . The coordinates of point A are ( 4 , 0 ) .
  2. Point B is on the y -axis at y = 2 . The coordinates of point B are ( 0 , 2 ) .
  3. Point C is on the x -axis at x = 3 . The coordinates of point C are ( 3 , 0 ) .
  4. Point D is on the y- axis at y = 1 . The coordinates of point D are ( 0 , 1 ) .

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Practice Key Terms 7

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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