A plane is a two-dimensional flat unbounded region. The shortest distance between any two points on a plane lies on the plane itself. A coordinate system requires two numbers or quantities to define a unique position on the plane. One way to do this is to have two axes perpendicular to one another. Where the axes intersect is usually called the origin which allows the plane to be subdivided into 4 regions or quadrants and a point is defined by a measurement to the right (positive) or left (negative) of the origin on one axis, and above (positive) or below (negative) for the other axis. These pairs of numbers or quantities are called coordinates. The positive quadrant Q1 contains all points where both coordinates are positive. Q3 contains points where both coordinates are negative. The quadrants are labelled anticlockwise.
Polar coordinates have an arbitrary origin and a reference line and use two numbers or quantities. A radius emanates from the origin at an angle to an arbitrary reference line. The length of the radius arm and the angle the arm makes with the reference line are the two numbers or quantities defining every point in the plane.