Name
IÿÿIÿ,
Date
MDL
Period
Fill in Notes 1.3
Notes 1.3 - Midpoint & Distance Formulas
**Remember:ÿ To find the
from one endpoint to another on
a number line use the YVÿ,/ÿ'
ÿII '
AB- )
,Ir)lilÿ/l!ÿ, - the midpoint of a segment is the point that (I,lÿ'ÿl!ÿ
the segment into 'ÿJ!) congruent( ÿ" )segments.
the midpoint M of PQ is the point
between P and Q such that PM = MQ
Number Line Midpoint Formula:
To determine the midpoint on a number line add the two endpoints
and divide by 2.
EX 1:
-10
X
-9
-8
-7
-6
-5
-4
A
-3
-2
Y
-1
0
1
2
B
3
4
What is the coordinate of the midpoint of AB?
What is the coordinate of the midpoint XY?
5
6
7
8
9
10
/ÿi,l,ÿ
meoosto
A ÿI,[ÿW\Oÿ- /0!ÿ is a point, r aÿ, !inÿ, line segment, or plane that
/VÿO(ÿ . a segment at its ÿ/ÿlÿ(ÿJ/tt/ÿ, .. A midpoint or segment
bisector bisects a segment.
EX 2: Line RM bisects LK at point D. Find DK if LK is 16 inches.
g !
EX 3: If P is the midpoint of C--D and PC = x and PD = 5x - 4, find the value of x and the measure
of CD.
\
I
EX 4: L is between H and Z. Q is the midpoint of H--L. L--Z is twice as long as HQ. HL = 7x - 5
and HQ = x + 5. Find HQ and HZ.
!
Coÿoÿdordinate plane midpoint formula:
The coordinates of the
endpoints are (xl, yÿ) and
of a segment whose
2, y2) are
EX 5: The endpoints of RS are R(1, -3) and S(4, 2). Find the midpoint•
EX 6: The midpoint of RQ in the graph below is P(4, -1).
lrTt-r
Find the coordinates of R if Q is at (3,-2)
t-ÿ-
/ { i i i ; i
/v
:
ÿ
ÿ ;} 7:
.>,,ÿ
!
....... !
: g "
ill :: ÿ
li! i;)
t
.ÿLJ
ÿ i-;-i i
EX 7: What happens when you are missin_q an endpo,nt? .ÿ \tÿ}!t blj!ÿ{,/
The midpoint of JK is M(-2.5,-1•5). One endpoint is J(-6,13). /lFind the coordinates of endpoint K..
p-iÿ :
, : :
Coordinate Plane Distance Formula:
The ÿ ÿ (ÿ] ........ between two points (xl, yl) and (xz, yz) on a coordinate
plane can be found using the (ÿSJTL/ti(Uv Jÿ !i V!/t !,l (7 #,J
EX 8: What is the exact length of segment RS if R(3 2) and S(4, 3)
'i
EX 9: Determine if the two segments AB and LK are congruent
AB" A(1,2);B(3,3)
2
4
LK : L(1,!);K(2,1)