Coordinates, Distance, and Midpoint

Coordinate Plane

The coordinate plane is defined by two perpendicular lines called axes, which divide the coordinate plane into four quadrants. Any point in the coordinate plane can be located by an ordered pair of values (x,y)\left(x, y\right).

A coordinate plane is a plane that is used to locate points by using coordinates (x,y)\left(x, y\right) that give the distance from the xx-axis and the yy-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 (0,0)(0, 0).

Each location or point in the coordinate plane can be written as an ordered pair, which is a pair of numbers written in order, (x,y)\left(x, y\right), 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 xx-coordinate is negative, move left. If it is positive, move right. If the yy-coordinate is negative, move down. If it is positive, move up.

Plotting Ordered Pairs

(4,6)(4, 6) (3,4)(-3, 4) (2,5)(-2, -5)
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 xx- and yy-axis. The quadrants are numbered I, II, III, and IV. Quadrant I is above the xx-axis and to the right of the yy-axis, where both coordinates are positive. From there, the quadrants are labeled counterclockwise around the origin.

  • In Quadrant I, xx is positive, and yy is positive.
  • In Quadrant II, xx is negative, and yy is positive.
  • In Quadrant III, xx is negative, and yy is negative.
  • In Quadrant IV, xx is positive, and yy is negative.
A point may be in one of the four quadrants, on an axis, or at the origin. The xx- and yy-coordinates of a point are either positive or negative depending on which quadrant it is located. Points that lie on the xx- or yy-axis are not in any quadrant.