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DefinitionCoordinate SystemsCoordinates
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Definition  Coordinate Systems  Coordinates
This is part of a collection of definitions related to coordinate systems and related topics. This includes general definitions for coordinate systems, as well as examples of specific coordinate systems and properties of those systems.
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The following section includes background information on the Cartesian coordinate plane.
Integers on the Cartesian Coordinate Plane
The video was uploaded on 11/15/2022.
You can view the video here.
The video lasts for 6 minutes and 44 seconds.
Video Transcript
You’ve seen how to add, subtract, multiply, and divide integers. You have also seen how to simplify expressions with integers. In this video we look at using integers to graph points on the Cartesian coordinate plane.
Let’s start with an example.
A construction truck goes from Building A to Building B to Building C. Describe the coordinates of these buildings.
Notice the Cartesian coordinate system. Here is the yaxis and here is the xaxis. This happens to just show Quadrant I.
This truck goes from point A here to point B here to point C here. These three points can be graphed with integer coordinates.
Here is a version of the graph with just the points. Where the x and yaxes intersect is the origin, which has coordinates (0, 0).
Let’s assume that each tic mark along the horizontal and vertical axes represent 1 unit. Let’s look at point A. We start at the origin and count one unit along the xaxis until we are aligned with A. Now we move up 2 units to get to the point. So, point A has coordinates (1, 2).
This number is the xcoordinate and this number is the ycoordinate. Now let’s look at point B.
Start at the origin and count the number of tic marks along the xaxis to align with B. There are 12345678 units. And we move up 2 units. So point B has coordinates (8, 2).
Now let’s move on to point C. First thing, notice that it is vertically aligned with point B, which we know has an xcoordinate of 8. So C has an xcoordinate of 8. Starting here let’s count up to get to C. There are 12345 tic marks. So C has coordinates (8, 5).
Let’s look at another example.
A diver takes a dive and his path is shown in the red dotted line. He passes through points A, B, and C. What are the coordinates of those points?
We can use positive and negative integers to show the coordinates of the diver at the three points. Here is a clean version to make it easier to identify the coordinates.
Recall that where the x and y axes intersect is the origin, which has coordinates (0, 0). This coordinate system shows Quadrant I here and Quadrant II here. Quadrant I has all positive coordinates. Quadrant II has positive x and negative y coordinates.
Let’s assume that each tic mark along the horizontal and vertical axes represent 1 unit. Let’s look at point A. We start at the origin and count one unit along the xaxis until we are aligned with A. There are 12345678910 units. Now we move up 1234 units to get to the point. So, point A has coordinates (10, 4).
Now let’s look at point B. Notice that the point is on the xaxis. Any point on the xaxis has zero as a ycoordinate. So we just need t find the xcoordinate.
Start at the origin and count one unit along the xaxis until we are aligned with B, There are 123456789101112131415 units. So point B has coordinates (15, 0).
Now let’s move on to point C. First thing, notice that it is just one unit to the right of point B. Since point B has an xcoordinate of 15, then C has an xcoordinate of 16. Now we count down 1234 units along the yaxis. Four units below the xaxis makes the xcoordinate 4. So point C has coordinates (16, 4).
Let’s look at a final example.
Find the coordinates of points A, B, C, and D, which are the corners of a rectangle.
Notice that this rectangle is centered at the origin. What this means is that the yaxis splits the rectangle into equal sections. The same thing happens with the xaxis: It splits the rectangle into two equal sections this way.
This means that the rectangle is symmetric about the xaxis and the yaxis. Now we can look at the coordinates for the four points to see how this symmetry is reflected in the coordinates.
Notice that positive and negative 7 and 3 are integers that make up these coordinates. Look at any collinear pair of coordinates and you’ll see that pairs of coordinates are opposites. For example, A and B have opposite xcoordinates, while D and C also have opposite xcoordinates. AD and BC have opposite ycoordinates.
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Common Core Standards  CCSS.MATH.CONTENT.6.G.A.3, CCSS.MATH.CONTENT.5.G.A.1, CCSS.MATH.CONTENT.5.G.A.2, CCSS.MATH.CONTENT.6.NS.C.6.C, CCSS.MATH.CONTENT.8.G.A.3 

Grade Range  5  8 
Curriculum Nodes 
Geometry • Coordinate Geometry • Coordinate Systems 
Copyright Year  2021 
Keywords  defnitions, glossary terms, coordinate geometry, ordered pair, coordinates, quadrant 