1. Distance Formula & Midpoint of a Segment
Tutorial 12e

2. The Distance Formula
The distance d between two points A (x1,y1) and B (x2,y2) is:
(x1,y1)A
B(x2,y2)

3. Example Distance Problem
The graph shows Juan’s newspaper route.
Find the distance between Parker and Commonwealth in miles.
(3,2)
(1,-3)
(-3,-4)
The distance between Parker and Commonwealth is 5.4 miles

4. If AM  MC, then M is the midpoint of AC.
A midpoint of a segment is a point that divides a segment into two congruent segments. A M C
If AM  MC, then M is the midpoint of AC.

5. The Midpoint Formula
The coordinates of the midpoint M of AB with the endpoints A (x1,y1) and B (x1,y2) are the following: •
A(x1,y1)
B(x2,y2) •

6. Example Midpoint Problem
Find the coordinate of the midpoint of segment JS.
Step 1:
First you must locate the coordinates of the two endpoints of segment JS.
(x1,y1)
(-3,2)
(- 1/2, 1/2 ) •
J has a coordinate of (-3,2)
S has a coordinate of (2,-1)
(2,-1)
(x2,y2)
Step 2:
Substitute the coordinates into the midpoint formula, then solve. ÷ ø ö ç è æ + = 2 , 1 y x M
The coordinate of the midpoint of JS is

7. ÷ ø ö ç è æ + = 2 , 1 y x M
Remember:
Check your Answers

8. ÷ ø ö ç è æ + = 2 , 1 y x M
Remember:

9. The End
Time to move on
to the assignment or
the next lesson