Sullivan Algebra and Trigonometry: Section 2.1 Rectangular Coordinates Objectives Use the Distance Formula Use the Midpoint Formula

We define the rectangular or Cartesian coordinate system as the plane formed by two number lines, the x-axis and y-axis, intersecting at a right angle. Points in the xy-plane are located and labeled using ordered pairs (x,y), called the coordinates of a point. (4,5) (-2,-4)

The four regions in the x-y plane are known as quadrants, labeled as follows: x y Quadrant I x > 0, y > 0 Quadrant IV x > 0, y < 0 Quadrant III x < 0, y < 0 Quadrant II x 0

Theorem: Distance Formula The distance between two points  P xy 1 11 , and  P xy 222 ,, denoted by  dPP 1 2, is

Example: Find the distance between the points (3,8) and (-1,2)

Theorem: Midpoint Formula