1.7 Midpoint and Distance in the Coordinate Plane 9/22/10

• You can use formulas to find the midpoint and the length of any segment in the coordinate plane.

Number Line Coordinate Plane

2

a bM

1 2 1 2,2 2

x x y yM

Finding the Midpoint• Segment AB has endpoints at -4 and 9. What

is the coordinate of its midpoint?

2

a bM

4 9

2M

5

2M 2.5

Finding the Midpoint• Segment EF has endpoints E (7 , 5) and

F (2 , -4). What are the coordinates of its midpoint M?

1 2 1 2,2 2

x x y yM

7 2 5 ( 4)

,2 2

M

9 1,2 2

M

(4.5,0.5)M

Finding an Endpoint• The midpoint of segment CD is M(-2 , 1). One

endpoint is C (-5 , 7). What are the coordinates if the other endpoint D?

2 25 7( 2,1) ,

2 2

x y 25

22

x

24 5 x

21 x

271

2

y

22 7 y

25 y (1, 5)D

Distance Formula• The distance between two points A(x1 , y1) and

B(x1 , y1) is2 2

2 1 2 1( ) ( ) .d x x y y

Finding Distance• What is the distance between U(-7 , 5) and

V(4 , -3)? Round to the nearest tenth?

2 22 1 2 1( ) ( )d x x y y

2 2(4 ( 7)) ( 3 5)d

2 2(11) ( 8)d

121 64

185 13.6

More Practice!!!!!

• Classwork – Textbook p. 54 #7 – 29 odd.

• Homework – Textbook p. 54 #6 – 30 even.