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2.1 Segment Bisectors

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2.1 Segment Bisectors

- Midpoint – the point on the segment that divides it into two congruent segments

A

M

B

- Segment bisector – a segment, line, ray, or plane that intersects a segment at its midpoint
- Bisect – to divide the segment into two congruent segments

C

A

M

B

D

- M is the midpoint of AB. Find AM and MB.
- AM = MB = ½ (AB)
- = ½ (26)
- = 13

26

A

M

B

- P is the midpoint of RS. Find PS and RS.
- RP = PS so PS = 7
- RS = 2 (RP)
- = 2 (7)
- = 14

R

P

S

7

- Line l is a segment bisector of AB. Find x.
AM = MB

5x = 35

x = 7

5x

35

A

M

B

l

- The coordinates of the
midpoint of a segment

are the averages of the

x-coordinates and the

y-coordinates of the

endpoints

B

y2

y1 + y2

----------

2

M

A

y1

x1

x1 + x2

---------

2

x2

- The coordinates of the
midpoint of AB is:

M x1 + x2 , y1 + y2

2 2

B

y2

y1 + y2

----------

2

M

A

y1

x1

x1 + x2

---------

2

x2

B (7, 4)

M

A (1, 2)

1

1

Let (x1, y1) = (1, 2)

Let (x2, y2) = (7, 4)

M = 1 + 7 , 2 + 4

2 2

= (4, 3)

- Pg. 56 # 1-10