1.3 Key
Concepts
Midpoint
The Point that divides the
segment into two congruent
segments.
Segment Bisector
A Point, Ray, Line, Line
Segment, or Plane that
intersects the segment at its
Midpoint
Midpoint Formula
[(x
1
+
x
2
)/2]
,
[(y
1
+
y
2
)/2]
Distance Formula
AB = √[(x
2
x
1
)
2
+ (y
2

y
1
)
2
]
In the skateboard design,
VW
bisects
XY
at point
T
,
and
XT
=
39.9
cm
. Find
XY
.
Skateboard
SOLUTION
EXAMPLE 1
Find segment lengths
Point
T
is the midpoint of
XY .
So
, XT = TY =
39.9
cm
.
XY
=
XT
+
TY
= 39.9 + 39.9
= 79.8
cm
Segment Addition Postulate
Substitute.
Add.
SOLUTION
EXAMPLE
2
Use algebra with segment lengths
STEP
1
Write and solve an equation. Use the fact
that
VM
=
MW
.
VM
=
MW
4
x
–
1
=
3
x
+ 3
x
– 1 = 3
x
= 4
Write equation.
Substitute.
Subtract
3
x
from each side.
Add
1
to each side.
Point
M
is the midpoint
of
VW
. Find the length of
VM
.
ALGEBRA
EXAMPLE
2
Use algebra with segment lengths
STEP
2
Evaluate the expression
for
VM
when
x
=
4
.
VM
= 4
x
– 1 = 4(4) – 1
= 15
So, the length of
VM
is
15.
Check:
Because
VM
=
MW
,
the length of
MW
should be
15
. If you evaluate the expression for
MW
, you should
find that
MW
= 15
.