Transcript File

Midpoint and Distance in the Coordinate
Plane
• You can use formulas to find the midpoint and the
length of any segment in the coordinate plane.
Number Line
M 
ab
2
Coordinate Plane
 x1  x 2 y 1  y 2 
M 
,

2
2


Finding the Midpoint
• Segment AB has endpoints at -4 and 9. What
is the coordinate of its midpoint?
M 
ab
2
M 
4  9
2
M 
5
2
 2 .5
Finding the Midpoint
• Segment EF has endpoints E (7 , 5) and
F (2 , -4). What are the coordinates of its
midpoint M?
 x1  x 2 y 1  y 2 
M 
,

2
2


 7  2 5  (4) 
M 
,

2
 2

9 1
M  , 
2 2
M (4.5, 0.5)
Finding the Midpoint
Find the coordinates of the midpoint of EF
with endpoints E(–2, 3) and F(5, –3).
Finding the Midpoint
Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).
= (–5, 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 

2 
5  x2
2
1
7  y2
2
4  5  x2
2  7  y2
1  x2
5  y2
D (1,  5)
Finding an Endpoint
• M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find the
coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:
Finding an Endpoint
Step 3 Find the x-coordinate.
Set the coordinates equal.
Multiply both sides by 2.
12 = 2 + x
– 2 –2
Simplify.
Subtract.
10 = x
Simplify.
The coordinates of Y are (10, –5).
2=7+y
– 7 –7
–5 = y
Distance Formula
• The distance between two points A(x1 , y1) and
B(x1 , y1) is
d 
( x 2  x1 )  ( y 2  y 1 ) .
2
2
Finding Distance
• What is the distance between U(-7 , 5) and
V(4 , -3)? Round to the nearest tenth?
d 
d 
d 
( x 2  x1 )  ( y 2  y 1 )
2
2
(4  (  7 ))  (  3  5)
2
(11)  (  8)
2
2

121  64

185  1 3 .6
2