1.5 Segment Bisectors &

Midpoint

ALGEBRA 1B UNIT 11: DAY 7

Segment Bisector

• A segment, ray, line, or plane that intersects a segment at its midpoint.

A

BM

k

SEGMENT BISECTOR CONSTRUCTION DEMO

http://www.mathopenref.com/constbisectline.html

SEGMENT BISECTOR PRACTICE

• USING A COMPASS & RULER,

CONSTRUCT THE SEGMENT BISECTOR FOR EACH PROBLEM ON THE WORKSHEET BEING PASSED OUT.

• COMPARE ANSWERS WITH YOUR NEIGHBOR.

Midpoint

• The point that bisects a segment.

• Bisects?

splits into 2 equal pieces

A M B 12x+3 10x+5

12x+3=10x+5

2x=2

x=1

Ex1: Solve for x.

If they are congruent, then set their measures equal to each other!

A M B

4x-1 9x - 2

4x-1 = 9x-2

-1 = 5x -2

1 = 5x

= x

#2 you try!!: Solve for x.

5

1

Midpoint Formula

2,

22121 yyxx

Ex3: Find the midpoint of SP if S(-3,-5) & P(5,11).

2

115,

2

53

2

6,2

2

3,1

#4 you try: Find the midpoint of SP if S(2,-5) & P(-1,-13).

2

)13(5,

2

)1(2

2

18,2

1

9,2

1

Ex #5: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.

)midpoint(2

,2

2121

yyxx

22

21 xx

42

21 yy

22

1 2 x

42

7 2 y

41 2 x 87 2 y

52 x 12 y

1,5

#6 you try!!: The midpoint of AB is M(1,-4). One endpoint is A(3,9). Find the coordinates of B.

)midpoint(2

,2

2121

yyxx

12

21 xx

42

21 yy

12

3 2 x

42

9 2 y

23 2 x 89 2 y

12 x 172 y

17,1