1. 1.3 Segments, Midpoints and distance formula
Geometry
1.3 Segments, Midpoints and distance formula
Essential Question: How can you determine the midpoint between two points?

2. Geometry 1.3 Segment,Midpoints and Distance formula
1.3 Topic/Objectives
Know what a bisector is
Use the midpoint formula
Solve problems with segment bisectors.
Use the distance formula
Geometry 1.3 Segment,Midpoints and Distance formula

3. Geometry 1.3 Segment,Midpoints and Distance formula
M is the midpoint of segment AC.
M bisects segment AC.
Bisect: divide into two congruent parts.
Congruence marks indicate congruent segments.
Geometry 1.3 Segment,Midpoints and Distance formula

4. A Segment Bisector can be a…
ray
line
Plane
Geometry 1.3 Segment,Midpoints and Distance formula

5. Geometry 1.3 Segment,Midpoints and Distance formula
Midpoint Formula
(x2, y2)
The midpoint is the average point. M
(x1, y1)
Geometry 1.3 Segment,Midpoints and Distance formula

6. Geometry 1.3 Segment,Midpoints and Distance formula
Midpoint Example
Find the midpoint of segment AB if A is point (10, -6) and B is point (2, 8).
Solution:
(6, 1)
Geometry 1.3 Segment,Midpoints and Distance formula

7. Geometry 1.3 Segment,Midpoints and Distance formula
Your Turn
Find the midpoint of the segment between (20, -14) and (-16, 4).
Solution:
(2, -5)
Geometry 1.3 Segment,Midpoints and Distance formula

8. Another midpoint problem
The midpoint of segment DH is O(3, 4). One endpoint is D(5, 7). Find the coordinates of H.
D(5,7)
Write out the formula:
O(3,4)
H(x, y)
continues…
Geometry 1.3 Segment,Midpoints and Distance formula

9. midpoint problem continued
There are two equations to solve:
Solve:
Solve:
continues…
Geometry 1.3 Segment,Midpoints and Distance formula

10. midpoint problem continued
Since x = 1 and y = 1, the other endpoint is H(1,1).
D(5,7)
O(3,4)
H(1, 1)
Geometry 1.3 Segment,Midpoints and Distance formula

11. Geometry 1.3 Segment,Midpoints and Distance formula
Your Turn
The midpoint of segment AB is M(1, 5). If one endpoint is A(-3, -4), find the coordinates of B.
Solution:
is the midpoint.
Solve for x:
Solve for y:
Endpoint
(5, 14)
Geometry 1.3 Segment,Midpoints and Distance formula

12. Geometry 1.3 Segment,Midpoints and Distance formula
Geometry 1.3 Segment,Midpoints and Distance formula

13. EX: Find distance between R and S. Round to nearest tenth if needed.
Geometry 1.3 Segment,Midpoints and Distance formula