9.1 Apply the Distance and
Midpoint Formulas
Algebra II
Geometry Review!
• What is the difference between the
symbols AB and AB?
Segment AB
The length of
Segment AB
The Distance Formula
• The Distance d
between the points
(x1,y1) and (x2,y2) is :
d  ( x2  x1 )  ( y2  y1 )
2
2
1)Find the distance between the
two points.
•
•
(-2,5) and (3,-1)
Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)
d  (3  (2))  (1  5)
2
d  25  36
d  61  7.81
2
2)Classify the Triangle using the
distance formula (as scalene,
isosceles or equilateral)
A: (4.00, 6.00)
AB  (6  4) 2  (1  6) 2  29
A
C: (1.00, 3.00)
BC  (1  6) 2  (3  1) 2  29
C
B
B: (6.00, 1.00)
AC  (1  4) 2  (3  6) 2  3 2
Because AB=BC the triangle is ISOSCELES
The Midpoint Formula
• The midpoint between the two
points (x1,y1) and (x2,y2) is:
x2  x1 y2  y1
M (
,
)
2
2
3)Find the midpoint of the segment
whose endpoints are (6,-2) & (2,-9)
 6  2  2  9 
,


2 
 2
  11 
 4,

2 

Steps to write an equation in slope-intercept form for
the perpendicular bisector of the segment
•
•
•
•
•
1.) Find the midpoint of segment
2.) Find the slope of segment
3.) Write the opposite & reciprocal slope.
4.) Use either point-slope formula or
slope intercept form (2)
4)Write an equation in slopeintercept form for the perpendicular
bisector of the segment whose
endpoints are C(-2,1) and D(1,4).
• First, find the midpoint of CD.
(-1/2, 5/2)
• Now, find the slope of CD.
m=1
* Since the line we want is perpendicular to
the given segment, we will use the
opposite reciprocal slope for our equation.
(y-y1)=m(x-x1)
or
y=mx+b
Use (x1 ,y1)=(-1/2,5/2) and m=-1
(y-5/2)=-1(x+1/2)
or
5/2=-1(-1/2)+b
y-5/2=-x-1/2
or
5/2=1/2+b
y=-x-1/2+5/2
or
5/2-1/2=b
y=-x+2
or
2=b
y=-x+2
Assignment