The Distance and Midpoint
Formulas
Topic 7.1
Distance Formula

Used to find the distance between two points
distance  ( x2  x1 )  ( y2  y1 )
2
2
Example

Find the distance between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)
distance  ( x2  x1 )  ( y2  y1 )
2
distance  (1  4)  (12  8)
2
distance  (3)  (4)
2
2
2
distance  9  16  25 
5
2
YOU TRY!!

Find the distance between:

A. (2, 7) and (11, 9)
(9)  (2)  85
2

2
B. (-5, 8) and (2, - 4)
(7)  (12)  193
2
2
Midpoint Formula

Used to find the center of a line segment
 x2  x1 y2  y1 
midpoint  
,

2 
 2
Example

Find the midpoint between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)
 x2  x1 y2  y1 
midpoint  
,

2 
 2
 1  4 12  8 
midpoint  
,

2 
 2
midpoint   5 ,10 


2


YOU TRY!!

Find the midpoint between:

A)
(2, 7) and (14, 9)
midpoint = 8,8

B)
(-5, 8) and (2, - 4)
 -3 
midpoint =  , 2 
2 