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

2. 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)

3. 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

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

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

6. Theorem: Midpoint Formula