1. 2.1 Segment Bisectors

2. Definitions Midpoint – the point on the segment that divides it into two congruent segments ABM

3. Definitions Segment bisector – a segment, line, ray, or plane that intersects a segment at its midpoint Bisect – to divide the segment into two congruent segments ABM D C

4. Find Segment Lengths M is the midpoint of AB. Find AM and MB. AM = MB = ½ (AB) = ½ (26) = 13 ABM 26

5. Find Segment Lengths P is the midpoint of RS. Find PS and RS. RP = PS so PS = 7 RS = 2 (RP) = 2 (7) = 14 RSP 7

6. Use Algebra with Segment Lengths Line l is a segment bisector of AB. Find x. AM = MB 5x = 35 x = 7 ABM l 5x35

7. The Midpoint Formula The coordinates of the midpoint of a segment are the averages of the x-coordinates and the y-coordinates of the endpoints A M B y2y2 y 1 + y 2 ---------- 2 y1y1 x1x1 x 1 + x 2 --------- 2 x2x2

8. The Midpoint Formula The coordinates of the midpoint of AB is: M x 1 + x 2, y 1 + y 2 2 2 A M B y2y2 y 1 + y 2 ---------- 2 y1y1 x1x1 x 1 + x 2 --------- 2 x2x2

9. Example 1 1 A (1, 2) B (7, 4) M Let (x 1, y 1 ) = (1, 2) Let (x 2, y 2 ) = (7, 4) M = 1 + 7, 2 + 4 2 2 = (4, 3)

10. Guided Practice Pg. 56 # 1-10