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The rectangular coordinate plane

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The rectangular coordinate plane
Before we learned to used Cartesian Coordinates, derived from the name
of a French mathematician, René Descartes, we first used the number line to
represent a pair of numbers.
A number line is the basic form of a mathematical graph using a straight
line with numbers corresponding to a point on the number line. A number line
extends in both directions and increase in value from left to right.
Coordinate system is a system for identifying points in space by labeling
them with numbers called coordinates. The Cartesian Coordinates is the most
commonly used coordinate system.
Cartesian Coordinate Plane is composed of a horizontal number line, x-
axis, and a vertical number line, y-axis. These lines have infinite values that are
each represented as a point on a number line. The two lines intersect at the
origin or the point where both values for x and y are equal to 0. Any point
anywhere on the plane is represented as a coordinate taking up the form (x, y).
Thus, the origin has the coordinate (0, 0).
There are four regions formed
in the coordinate plane. These
regions are called quadrants.
In Quadrant I, both values of
Points x and y are positive, (+, +).
In Quadrant II, Point x has
negative value and point y has
positive value, (-, +).
In Quadrant III, both values of
Points x and y are negative, (-, -).
In Quadrant IV, Point x has positive
value point y has negative value, (+, -).
In the Cartesian Coordinate
System, a point on the plane whose
coordinates are (3,5), refers to a point
located three units to the right of y-axis
called the abscissa or the x-coordinate
and the five units refer to a point
located above the x-axis called the
ordinate or the y-coordinate.
The point of the intersection of
the two axes is known as the origin and
the point (3, 5) in a coordinate plane is
called an ordered pair.

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The rectangular coordinate plane

  • 2. Before we learned to used Cartesian Coordinates, derived from the name of a French mathematician, René Descartes, we first used the number line to represent a pair of numbers. A number line is the basic form of a mathematical graph using a straight line with numbers corresponding to a point on the number line. A number line extends in both directions and increase in value from left to right.
  • 3. Coordinate system is a system for identifying points in space by labeling them with numbers called coordinates. The Cartesian Coordinates is the most commonly used coordinate system. Cartesian Coordinate Plane is composed of a horizontal number line, x- axis, and a vertical number line, y-axis. These lines have infinite values that are each represented as a point on a number line. The two lines intersect at the origin or the point where both values for x and y are equal to 0. Any point anywhere on the plane is represented as a coordinate taking up the form (x, y). Thus, the origin has the coordinate (0, 0).
  • 4. There are four regions formed in the coordinate plane. These regions are called quadrants. In Quadrant I, both values of Points x and y are positive, (+, +). In Quadrant II, Point x has negative value and point y has positive value, (-, +).
  • 5. In Quadrant III, both values of Points x and y are negative, (-, -). In Quadrant IV, Point x has positive value point y has negative value, (+, -).
  • 6. In the Cartesian Coordinate System, a point on the plane whose coordinates are (3,5), refers to a point located three units to the right of y-axis called the abscissa or the x-coordinate and the five units refer to a point located above the x-axis called the ordinate or the y-coordinate. The point of the intersection of the two axes is known as the origin and the point (3, 5) in a coordinate plane is called an ordered pair.
  • 7. Example: Find the following points and determine its quadrant or axes. A (3, 4) = Quadrant I B (-3, 2) = Quadrant II C (-2, -4) = Quadrant III D (6, -3) = Quadrant IV E (0, 0) = origin