A coordinate plane is a plane that is used to locate points by using coordinates that give the distance from the -axis and the -axis. The coordinate plane is formed by the intersection of the x-axis, a horizontal number line, and the y-axis, a vertical number line. The axes are perpendicular and intersect at the origin, which is the point with coordinates .
Each location or point in the coordinate plane can be written as an ordered pair, which is a pair of numbers written in order, , that can be used to locate a point in the coordinate plane. The x-coordinate is the first value in the ordered pair, which determines the horizontal distance of a point from the origin. The y-coordinate is the second value of the ordered pair, which determines the vertical distance of a point from the origin.
To graph a point, begin at the origin. If the -coordinate is negative, move left. If it is positive, move right. If the -coordinate is negative, move down. If it is positive, move up.
Plotting Ordered Pairs
|From the origin, move 4 units right and 6 units up.||From the origin, move 3 units left and 4 units up.||From the origin, move 2 units left and 5 units down.|
The signs of the coordinates determine which quadrant the point lies in. A quadrant is one of four regions of the coordinate plane that are formed by the - and -axis. The quadrants are numbered I, II, III, and IV. Quadrant I is above the -axis and to the right of the -axis, where both coordinates are positive. From there, the quadrants are labeled counterclockwise around the origin.
- In Quadrant I, is positive, and is positive.
- In Quadrant II, is negative, and is positive.
- In Quadrant III, is negative, and is negative.
- In Quadrant IV, is positive, and is negative.