
A coordinate graph (often referred to as a coordinate axes or coordinate grid), is a twodimensional number line where the two lines are perpendicular to one another.
• The horizontal axis is the xaxis.
• The vertical axis is the yaxis.
• A location in the grid is referred to as an ordered pair (or as "the coordinates").
• The point where the axes intersect is called the origin labeled with ordered pair (0,0).
• An ordered pair lists the xaxis value first, followed by the yaxis value in the form (x, y).
• The axes in a coordinate grid form four sections called quadrants (quadrants I, II, III and IV).



Plotting points on a coordinate grid:
Remember that an ordered pair is in the form (x,y).
• first move left or right on the xaxis.
• then move up or down on the yaxis.
• plot the point where these locations intersect.
• label the point using an ordered pair (x, y)

Reflections of points:
Did you notice that the points (3,4) and (3,4), on the grid above, are reflections of one another over the y axis?
When two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Reflection over yaxis:
When a point is reflected over the yaxis, the xcoordinate changes its sign.
(2,4) becomes (2,4) or vice versa
Notice that the
point and its reflection are both two units horizontally away from the yaxis.
Reflection over the xaxis:
When a point is reflected over the xaxis, the ycoordinate changes its sign.
(3,2) becomes (3,2) or vice versa
Notice that the
point and its reflection are both two units vertically away from the xaxis.

Reflection over both axes:
A reflection over both axes is a combination of a reflection over the xaxis and a reflection over the yaxis (in either order).
Following the pattern shown at the right, the point (2,3) is first reflected over the xaxis, and is then reflected over the yaxis. The ending point, (2,3), is a reflection over both axes.
In a reflection over both axes, both coordinates change their signs.



Distance Between Points:
When working on a coordinates axes, the distance between points with the same xcoordinate or the same ycoordinate can be easily determined by counting the vertical segment units or horizontal segment units separating the points.
Remember that distance is always a positive quantity (or zero).
On the graph at the right, the distance from point A to point B can be counted to be 6 units.
Since we are determining horizontal distance, we are examining the change in the xcoordinates. We are looking to find the distance from x = 4 to x = 2.
On a number line, we can count the distance from 4 to 2 and get 6 (which is essentially how we counted on the grid).
We can also represent this concept using absolute value. 

Under Absolute Value, we saw that the distance between two values a and b can be
expressed
as  a  b  or  b  a . Applying this information, we can get  4  2  = 6 or  2  (4)  = 6.
This same approach can be used to find the distance from point C to point D. Since this distance is vertical, we are examining the ycoordinates. We need to find the distance from y = 1 to y = 3.
By counting, we find this distance to be 4 units.
Using absolute value, we have  1  (3)  = 4 or  3  1  = 4.
But what happens if the distance between the points is "diagonal" instead of vertical or horizontal (such as the distance from (2,3) to (4,5))?
We will have an answer to this question when we develop a friendship with the Pythagorean Theorem under the Geometry section. 
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