1. Sullivan Algebra and Trigonometry: Section 2.1
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:
Quadrant I
x > 0, y > 0
Quadrant IV
x > 0, y < 0
Quadrant III
x < 0, y < 0
Quadrant II
x < 0, y > 0

4. ( ) ( ) Theorem: Distance Formula The distance between two points P Px y 1 = , ( ) P x y 2 = ,
and
, denoted by ( ) d P 1 2 , is

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

6. Theorem: Midpoint Formula