Lesson 1-3:
Use Distance and Midpoint
Formulas
Midpoints and Bisectors:
• The midpoint of a segment is the point that
divides the segment into two congruent
segments.
• A segment bisector is a point, ray, line, line
segment, or plane that intersects the segment
at its midpoint.
In the skateboard design, V W bisects X Y at
point T, and XT = 39.9 cm. Find XY.
Line n bisects the segment. Find the
n
indicated length.
D
E
n
A
B
Find AB if BC = 5/8 cm
C
Find DF if EF= 9 ½ m
F
n
A
B
C
Find AB if AC = 21 inches
Point M is the midpoint of V W . Find the length
of V M .
Identify the segment bisector of
Then find PQ.
14
PQ
.
w
A
M
x + 20
Find AC
5x - 4
C
The Midpoint Formula:
If A(x1, y1) and B(x2, y2) are points in a coordinate
plane, then the midpoint M of A B has
coordinates
 x1  x 2 y1  y 2 
Midpoint (M) =
,


2
2


Ex: The endpoints of RS are R(1, -3) and S(4, 2). Find
the coordinates of the midpoint M.
Ex: The endpoints of GH are G(7, -2) and H(-5, -6). Find
the coordinates of the midpoint P.
Ex: The midpoint of JK is M(2, 1). One endpoint is J(1,
4). Find the coordinates of endpoint K.
Ex: The midpoint of AB is M(5, 8). One
endpoint is A(2, -3). Find the coordinates
of endpoint B.
Ex: The midpoint of AB is M(3, -4). One
endpoint is A(-4, -6). Find the coordinates
of endpoint B.
Distance Formula:
• To find the distance between two points, you will
always use the Distance Formula.
• The Distance Formula:
If A(x1, y1) and B(x2, y2) are points in a coordinate
plane, then the distance between A and B is
distance (d) =
( x 2  x1 )  ( y 2  y1 )
2
2
Ex: What is the approximate length of RS with endpoints
R(2, 3) and S(4, -1)? Round to the nearest tenth of a unit.
Ex: What is the approximate length of AB with
endpoints A(-3, 2) and B(1, -4)?
Round to the nearest tenth of a unit.
Find the length of the
segment. Round to the
nearest tenth of a unit.
The endpoints of two segments are given. Find
each segment length. Tell whether the segments
are congruent.
AB: A(-4, 0), K(4,8)
CD: C(-4, 2), D(3, -7)
Homework!
Pgs 19-21 #1, 3-20 all, 26-34 even, 43-45,
48, 49