Download Geometry 1.3 Segments, Midpoints and distance formula

Geometry
1.3 Segments, Midpoints
and distance formula
Essential Question: How can you
determine the midpoint between two
points?
1.3 Topic/Objectives
• Know what a bisector is
• Use the midpoint formula
• Solve problems with segment
bisectors.
• Use the distance formula
Geometry 1.3 Segment,Midpoints and Distance
formula
Midpoint
A
M
C
•M is the midpoint of segment AC.
•M bisects segment AC.
•Bisect: divide into two congruent parts.
•Congruence marks indicate congruent
segments.
AM  MC
Geometry 1.3 Segment,Midpoints and Distance
formula
A Segment Bisector can be a…
segment
ray
line
Plane
Geometry 1.3 Segment,Midpoints and Distance
formula
Midpoint Formula
M
(x1, y1)
(x2, y2) The midpoint
is the
average
point.
 x1  x2 y1  y2 
,


2 
 2
Geometry 1.3 Segment,Midpoints and Distance
formula
Midpoint Example
Find the midpoint of segment AB if A
is point (10, -6) and B is point (2, 8).
Solution:
 10  2  6  8   12 2 
,

   ,   (6,
2   2 2
 2
Geometry 1.3 Segment,Midpoints and Distance
formula
1)
Your Turn
Find the midpoint of the segment
between (20, -14) and (-16, 4).
Solution:
 20  (16)  14  4   4  10 
,

 ,
  (2, -5)
2
2  2 2 

Geometry 1.3 Segment,Midpoints and Distance
formula
Another midpoint problem
The midpoint of segment DH is O(3, 4). One
endpoint is D(5, 7). Find the coordinates of H.
D(5,7)
Write out the
formula:
O(3,4)
H(x, y)
 x5 y7
,


2 
 2
continues…
Geometry 1.3 Segment,Midpoints and Distance
formula
midpoint problem continued
There are two equations to solve:
x5
3
2
Solve:
y7
4
2
Solve:
x5
3
2
x5  6
y7
4
2
y7 8
x 1
y 1
continues…
Geometry 1.3 Segment,Midpoints and Distance
formula
midpoint problem continued
Since x = 1 and y = 1, the other endpoint is
H(1,1).
D(5,7)
O(3,4)
H(1, 1)
Geometry 1.3 Segment,Midpoints and Distance
formula
Your Turn
The midpoint of segment AB is M(1, 5).
If one endpoint is A(-3, -4), find the
coordinates of B.
Solution:  x  (3) , y  (4)  is the midpoint.

2
2
Solve for x:
x 3
1
2
x 3  2
x5
Endpoint

Solve for y:
y4
5
2
y  4  10
(5, 14)
Geometry 1.3 Segment,Midpoints and Distance
formula
y  14
Distance Formula
Geometry 1.3 Segment,Midpoints and Distance
formula
EX: Find distance between R and S. Round to
nearest tenth if needed.
Geometry 1.3 Segment,Midpoints and Distance
formula