Transcript 1.7 Midpoint and Distance in the Coordinate Plane

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
ab
M 
2
Coordinate Plane
 x1  x2 y1  y2 
M
,

2 
 2
Finding the Midpoint
• Segment AB has endpoints at -4 and 9. What
is the coordinate of its midpoint?
ab
M 
2
4  9
M 
2
5
 2.5
M 
2
Finding the Midpoint
• Segment EF has endpoints E (7 , 5) and
F (2 , -4). What are the coordinates of its
midpoint M?
 x1  x2 y1  y2 
M
,

2 
 2
 7  2 5  ( 4)  M  9 , 1 
M
,



2 
 2
2 2
M (4.5,0.5)
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?
 5  x2 7  y2 
( 2,1)  
,

2 
 2
5  x2
2 
2
7  y2
1
2
4  5  x2
2  7  y2
1  x2
5  y2
D(1, 5)
Distance Formula
• The distance between two points A(x1 , y1) and
B(x1 , y1) is
d  ( x2  x1 )  ( y2  y1 ) .
2
2
Finding Distance
• What is the distance between U(-7 , 5) and
V(4 , -3)? Round to the nearest tenth?
d  ( x2  x1 )2  ( y2  y1 ) 2
d  (4  ( 7))  ( 3  5)
2
d  (11)  ( 8)
2
2
 121  64
 185  13.6
2
More Practice!!!!!
• Classwork – Textbook p. 54 #7 – 29 odd.
• Homework – Textbook p. 54 #6 – 30 even.