Coordinate Geometry Basics

Cartesian Plane and Graphing

• A pair of real numbers can be identified as an ordered pair.

Rectangular Coordinate Plane

• The Cartesian plane consists of two number lines (x-axis and y-axis) that intersect at right angles at the point O (origin).
• The x-axis and y-axis divide the plane into four quadrants.

Locating Points in the Rectangular Plane

• An ordered pair (a, b) can be located as a point in the rectangular plane:
  • a is the x-coordinate (abscissa)
  • b is the y-coordinate (ordinate)

Drawing Geometrical Shapes

• Various geometrical shapes can be drawn by joining a set of given points, such as:
  • Line segments
  • Triangles
  • Rectangles
  • etc.

Linear Equations

• A table can be constructed for pairs of values satisfying a linear equation in two variables.

Graphing Linear Equations

• The graph of a given linear equation can be drawn.

Special Cases of Linear Equations

• The graph of an equation of the form y = c can be drawn.
• The graph of an equation of the form x = a can be drawn.

Graphing Discrete Values

• A graph can be drawn from a given table of discrete values by choosing an appropriate scale.
• Not all first-degree equations form a linear graph; some may be a point graph.

Problem-Solving

• Problems related to linear graphs can be solved.