Quadrants and axes :
In mathematics, points are located in reference to two perpendicular number lines called axes.
Example 1 :
Write the ordered pair for point G.
Solution :
Follow along a vertical line through the point to find the x-coordinate on the x-axis. The x-coordinate is -4.
Follow along a horizontal line through the point to find the y-coordinate on the y-axis. The y-coordinate is 3.
So, the ordered pair for point G is (-4, 3). This can also be written as G(-4, 3).
The x-axis and y-axis separate the coordinate plane into four regions, called . Notice which quadrants contain positive and negative x-coordinates and which quadrants contain positive and negative y-coordinates. The axes are not located in any of the quadrants.
Signs of ordered pairs |
Lies in the quadrant | |
(+, +) (-, +) (-, -) (+, -) |
1st quadrant 2nd quadrant 3rd quadrant 4th quadrant |
When graphing an ordered pair, start at the origin. The x-coordinate indicates how many units to move right (positive) or left (negative). The y-coordinate indicates how many units to move up (positive) or down (negative).
If the x-coordinate value of the given point is 0, then the the given point will be located on y-axis. |
For example, the point (0,3) (0, -1) will be located on y-axis. | |
If the y-coordinate value of the given point is 0, then the the given point will be located on x-axis. |
For example, the point (5, 0) (-2, 0) will be located on x-axis. |
Example 2 :
Plot the given point on a coordinate plane.
A(3, 5)
Solution :
Both x and y-coordinate values are positive. So the given point will be located on the 1st quadrant.
Step 1 :
From origin, we have to move three units to the right side.
Step 2 :
Now move 4 units upward. .
Step 3 :
Draw a dot and label this point as (3, 5)
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