1.7 Midpoint and Distance in the Coordinate Plane
Download
Report
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
ab
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?
ab
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.