Page 2

Midpoint Formula

Coordinates of the midpoint: M =

2,

22121 yyxx

The midpoint is the average of the x’s and the average of the y’s

221 xx

xm

2

21 yyym

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

221 xx

xm

2

21 yyym

2

73 mx

2

4mx

2

64 my

2

10my

2,5-M

Down 2

Right 10

Down 1

Right 5

5,2

2mx 5my

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)

221 xx

xm

2

21 yyym

2

46 mx

2

10mx

2

108my

2

18my

5,9Midpoint

5mx 9my

k) (5c,2c) , (c,8c)

221 xx

xm

2

21 yyym

2

5 ccxm

2

6cxm

2

82 ccym

2

10cym

3c,5cMidpoint

cxm 3 cym 5

2. Find the abscissa of the midpoint of the line segment whose endpoints are:

a) (4,8) , (10,12)

221 xx

xm

2

104 mx

2

14mx

7Abscissam

7mx

b) (6,-6) , (12,-4)

221 xx

xm

2

126 mx

2

18mx

9Abscissa m

9mx

b) (8,-8) , (14,-4)

221 yy

ym

2

48 my

2

12my

6my

c) (6,-4) , (-9,1)

221 yy

ym

2

14 my

2

3my

3. Find the ordinate of the midpoint of the line segment whose endpoints are:

-6Ordinatem 2

3-Ordinate m

a) A(4,3) , M(4,9)

.point of scoordinate the find , and points of scoordinate Given the . ofmidpoint theis .8

BMA

ABMB (4,15)

B(4,15)

C) A(2,6) , M(0,3)

.point of scoordinate thefind , and points of scoordinate Given the . ofmidpoint theis .8

BMAABM

B(-2,0)

221 xx

xm

2

21 yyym

2

20 2x

220 x2

63 2y

266 y

20 y22 x

Graphically

B(-2,0)

M

Algebraically

e) A(5,-1) , M(-1,1)

B (-7,3)

M

.point of scoordinate thefind , and points of scoordinate Given the . ofmidpoint theis .8

BMAABM

Graphically

B(-7,3)

221 xx

xm

2

21 yyym

2

51 2x

252 x2

11 2y

212 y

23 y27 x

Algebraically

C) A(-4,6) , B(6,10)

s. of andr of value thefind

, ofmidpoint theis B If s).C(r, and B(6,10) A(-4,6), points Given the .9 AC

221 xx

xm

2

21 yyym

2

46

r

r 412

2

610

s

s620

s14r16

Algebraically

C(16,14)

Optional Check

HomeworkHomework

•Page 2

#4a,b,6a,7

a) A(3,4) , B(7,8)

. of scoordinate theFind circle. theofcenter theis anddiameter, a of endpoints are and circle, aIn .4

PPBA

P(5,6) 6,5

b) A(-5,-2) , B(3,7)

. of scoordinate theFind circle. theofcenter theis anddiameter, a of endpoints are and circle, aIn .4

PPBA

P(-1,2.5)

5.2,1

a) A(0,0) , B(10,0)

C(7,5) , D(3,5)

Down 5

Left 3

:ices with vertralquadrilate a of sides theof midpoints theFind .6

)0,5(ABM

)5.2,5.8(BCM

)5,5(CDM

)5.2,5.1(DAM

Down 5

Right 3

b) P(-3,3) , Q(11,3)

R(7,7) , S(1,7)

:ices with vertralquadrilate a of sides theof midpoints theFind .6

)3,4(PQM

)5,9(QRM

)7,4(RSM

)5,1(SPM

.point of scoordinate theFind (8,10).point of and (8,4) are point of scoordinate The . ofmidpoint theis .7

DMCCDM

)16,8(D

)16,8(D

.point of scoordinate theFind (8,10).point of and (8,4) are point of scoordinate The . ofmidpoint theis .7

DMCCDM

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

APPLIED QUIZ