Section 2.1

Cartesian Plane, Distance, and Midpoint

The distance between two points can be found by using the distance formula with the endpoints and

( ),x y1 1

( ),x y2 2

),( 11 yx ),( 22 yx

212

212 yyxxd

Find the distance between the points (2,1) and (4,5)

22 5142 d

22 42 d

164 d

20d

52d

Find the distance between (2, -1) and (-3, -6)

22 6132 d

22 55 d

2525 d

50d

25d

Midpoint of a Segment- Midpoint of a segment with endpoints and is given by:

A BM

AM = MB

),( 11 yx ),( 22 yx

2

,2

, 2121 yyxxyx mm

Find the midpoint of (2,3) and (4, 9)

Find the midpoint of (2,-3) and (-4, -6)

2

93,

2

42

2

12,

2

6 4,3

2

63,

2

42

2

9,

2

2

2

9,1