QUADRANTS AND AXES

About "Quadrants and axes"

Quadrants and axes :

In mathematics, points are located in reference to two perpendicular number lines called axes.

  • Points in the coordinate plane are named by ordered pairs of the form (x, y).
  • The first number, or x-coordinate, corresponds to the numbers on the x-axis.
  • The second number, or y-coordinate, corresponds to the numbers on the y-axis.
  • The origin, labeled O, has coordinates (0, 0).

Coordinate plane

Identifying points on a coordinate plane

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).

Plot the given points in a coordinate plane 

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)

After having gone through the stuff given above, we hope that the students would have understood "Quadrants and axes". 

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