Transcript Midpoint Formula - Camden Central School

Page 2
Midpoint Formula
The midpoint is the average of the x’s and the
average of the y’s
x1  x2
xm 
2
Coordinates of the midpoint:
y1  y 2
ym 
2
 x1  x2 y1  y 2 
M =
,

2 
 2
New Vocabulary:
Abscissa – the x value of an ordered pair
Ordinate – the y value of an ordered pair
Midpoint Formula
Given: A(3,4) and B(-7,6), find
the coordinates of midpoint M
x1  x2
2
3  7
xm 
2
4
xm 
2
xm 
y1  y 2
2
46
ym 
2
10
ym 
2
ym 
xm  2
M  - 2,5
ym  5
 2,5
Down 1
Down 2
Right 5
Right 10
How would you
get to the
midpoint?
1. Find the coordinates of the midpoint of the line segment that
joins each of the following pairs of points. (algebraically only)
a) (6,8) , (4,10)
x1  x2
2
64
xm 
2
10
xm 
2
xm  5
xm 
y1  y 2
2
8  10
ym 
2
18
ym 
2
ym  9
ym 
Midpoint 5,9
k) (5c,2c) , (c,8c)
x1  x2
2
5c  c
xm 
2
6c
xm 
2
xm  3c
xm 
y1  y 2
2
2c  8c
ym 
2
10c
ym 
2
ym  5c
ym 
Midpoint 3c,5c
2. Find the abscissa of the midpoint of the line segment
whose endpoints are:
a) (4,8) , (10,12)
x1  x2
2
4  10
xm 
2
14
xm 
2
xm  7
xm 
Abscissam  7
b) (6,-6) , (12,-4)
x1  x2
2
6  12
xm 
2
18
xm 
2
xm  9
xm 
Abscissa m  9
3. Find the ordinate of the midpoint of the line segment
whose endpoints are:
b) (8,-8) , (14,-4)
y1  y 2
2
 8  4
ym 
2
 12
ym 
2
ym  6
ym 
Ordinatem  -6
c) (6,-4) , (-9,1)
y1  y 2
2
 4 1
ym 
2
3
ym 
2
ym 
Ordinate m
-3

2
8. M is themidpointof AB. Given the
coordinates of pointsA and M , find
thecoordinates of point B.
a) A(4,3) , M(4,9)
B(4,15)
B (4,15)
8. M is themidpointof AB. Given thecoordinates of pointsA and M ,
find thecoordinates of point B.
Graphically
C) A(2,6) , M(0,3)
Algebraically
x1  x2
xm 
2
2  x2
0
2
0  2  x2
y1  y 2
2
6  y2
3
2
6  6  y2
ym 
0  y2
 2  x2
B(-2,0)
M
B(-2,0)
8. M is themidpointof AB. Given thecoordinates of pointsA and M ,
find thecoordinates of point B.
e) A(5,-1) , M(-1,1)
Graphically
Algebraically
x1  x2
2
5  x2
1 
2
 2  5  x2
xm 
y1  y 2
2
 1  y2
1
2
2  1  y2
ym 
3  y2
 7  x2
B(-7,3)
B (-7,3)
M
9. Given thepointsA(-4,6),B(6,10)and C(r,s). If B is themidpointof AC,
find the valueof r and of s.
Algebraically
C) A(-4,6) , B(6,10)
C(16,14)
x1  x2
xm 
2
4r
6
2
12  4  r
16  r
y1  y 2
2
6s
10 
2
20  6  s
ym 
14  s
Optional Check
Homework
•Page 2
#4a,b,6a,7
4. In a circle, A and B are endpointsof a diameter,and P is thecenter
of thecircle. Find thecoordinates of P.
a) A(3,4) , B(7,8)
P(5,6)
5,6
4. In a circle, A and B are endpointsof a diameter,and P is thecenter
of thecircle. Find thecoordinates of P.
b) A(-5,-2) , B(3,7)
P(-1,2.5)
1,2.5
6. Find themidpointsof thesides of a quadrilateral with vertices :
a) A(0,0) , B(10,0)
Left 3
C(7,5) , D(3,5)
M AB  (5,0)
M BC  (8.5,2.5)
M CD  (5,5)
M DA  (1.5,2.5)
Down 5
Right 3
Down 5
6. Find themidpointsof thesides of a quadrilateral with vertices :
b) P(-3,3) , Q(11,3)
R(7,7) , S(1,7)
M PQ  (4,3)
M QR  (9,5)
M RS  (4,7)
M SP  (1,5)
7. M is themidpointof CD. T hecoordinates of pointC are (8,4)
and of point M (8,10). Find thecoordinates of point D.
D(8,16)
D(8,16)
7. M is themidpointof CD. T hecoordinates of pointC are (8,4)
and of point M (8,10). Find thecoordinates of point D.
APPLIED QUIZ
1. Graph segment AB with
endpoints A(-4,-3) and B(4,-7).
A) Find the distance to the
nearest tenth.
B) Find the midpoint of AB
2. Given endpoint A (-3,5) and
midpoint M(0,3), find the
coordinates of the other endpoint B