<< Chapter < Page Chapter >> Page >

...

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.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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 ) .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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 ) .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

what is phylogeny
Odigie Reply
evolutionary history and relationship of an organism or group of organisms
AI-Robot
ok
Deng
what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 7

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask