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Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located:

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

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 1) is plotted and labeled

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Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located:

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

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 1) is plotted and labeled

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How do the signs affect the location of the points? You may have noticed some patterns as you graphed the points in the previous example.

For the point in [link] in Quadrant IV, what do you notice about the signs of the coordinates? What about the signs of the coordinates of points in the third quadrant? The second quadrant? The first quadrant?

Can you tell just by looking at the coordinates in which quadrant the point ( −2 , 5 ) is located? In which quadrant is ( 2 , −5 ) located?

Quadrants

We can summarize sign patterns of the quadrants in this way.

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-axes each run from negative 7 to 7. 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

What if one coordinate is zero as shown in [link] ? Where is the point ( 0 , 4 ) located? Where is the point ( −2 , 0 ) located?

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. Points (0, 4) and (negative 2, 0) are plotted and labeled.

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 ) .

Plot each point:

( 0 , 5 ) ( 4 , 0 ) ( −3 , 0 ) ( 0 , 0 ) ( 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-axes each run from negative 7 to 7. The points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0) are plotted and labeled.
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Plot each point:

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

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled.

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Plot each point:

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

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (negative 5, 0), (3, 0), (0, 0), (0, negative 1), and (0, 4) are plotted and labeled.

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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, when you write the ordered pair    use the correct order, ( x , y ) .

Name the ordered pair of each point shown in the rectangular coordinate system.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.

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 ) .

Point E is on the y -axis at y = −2 . The coordinates of point E are ( 0 , −2 ) .

Point F is on the x -axis at x = 3 . The coordinates of point F are ( 3 , 0 ) .

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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