Rectangular Coordinate System

Sometimes referred to as the rectangular coordinate system, the Cartesian coordinate system consists of two perpendicular real number lines intersecting at zero. Positions on this grid system are identified using ordered pairs, (x, y). The center of the system (0, 0) is called the origin. The x-coordinate indicates horizontal distance from the origin and the y-coordinate indicates vertical distance from the origin.

Instructional Video: Plotting Points on the Coordinate Plane

The horizontal number line, usually called the x-axis, is typically used for the independent variable. The vertical real number line, usually called the y-axis, is used for the dependent variable.

Ordered pairs with 0 as a coordinate do not lie in a quadrant; these points lie on an axis.

Example: Find the distance and midpoint between the two points: (3, 4) and (−1, 2).

Example: Find the distance and midpoint between the two points: (0, 0) and (−3, 4).

Example: Find the distance and midpoint between the two points: (−1,−1) and (1,1).

Example: Find the distance and midpoint between the two points: (−2,−5) and (−4,−3).

Circle Word Problem: If the diameter of a circle is defined by two points (−3, 4) and (7, 4), find the center and radius of the circle. (Hint: diameter = 2*radius)