2. The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal parts.

3. In Coordinate Geometry, there is more than one way to determine the midpoint of a line segment.  

4. Find the midpoints of line segments AB and CD.
Method 1
You may find the midpoint by simply dividing the length of the segment by 2 and counting that value from either of the endpoints.  
Find the midpoints of line segments AB and CD.
The length of line segment AB is 8 (by counting).  The midpoint is 4 units from either endpoint.  On the graph, this point is (1,4).
The length of line segment CD is 3 (by counting).  The midpoint is 1.5 units from either endpoint.  On the graph, this point is (2,1.5)

5. Method 2
If the line segments are diagonal, more thought must be paid to the solution.  When you are finding the coordinates of the midpoint of a segment, you are actually finding the average (mean) of the x-coordinates and the average (mean) of the y-coordinates.
-30
-20
-10 10 20 30 a b

6. Midpoint Coordinates =
Midpoint Formula
Midpoint Coordinates =
The Midpoint Formula works for all line segments:  vertical, horizontal or diagonal.

7. Example 1 - Find a Midpoint on a Number LineQ R -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Method 1
The distance from -3 to 4 is 7. Half of 7 is 3.5, which you add to -3. The midpoint is 0.5. +7
+3.5 Q R -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

8. Example 1 - Find a Midpoint on a Number LineQ R -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Method 2
Use the midpoint formula

9. Example 2 – Find the Coordinates of a Midpoint
TEMPERATURE Find the coordinate of the midpoint PQ
The coordinates of P and Q are -20 and 40. Let M be the midpoint of PQ
Q = 40
P = -20
Find the coordinates of M, the midpoint of PQ, for P(-1, 2) and Q(6, 1)
Let P be (x1, y1) and Q be (x2, y2)

10. Example 3 - A Different Problem Find the Coordinates of an Endpoint
Find the coordinates of X if Y(-2, 2) is the midpoint of XQ, and Q has the coordinates (2, 8)
Method 2
Let Z be (x2, y2) in the Midpoint Formula
Write two equations to find the coordinates of x

11. A Different Approach to a Different Problem
Find the Coordinates of an Endpoint
Find the coordinates of X if Y(-2, 2) is the midpoint of XQ, and Q has the coordinates (2, 8)
Method 1
First, let’s try to visualize the problem.
This will give you an idea of where X is located. Q Y

12. Example 3 – Use Algebra to Find Measures
A is the midpoint of segment BC.
Find x and the measures of AB
and AC.
2x + 14 C
3x + 6 A B

13. Exercises
Given the endpoints of a line segment, find the midpoint
1) (7 , 4), (9, −1) 2) (8, −9), (0, 5)
3) (1, −7), (1, −12) 4) (0, 4), (−4, -12)
5) (−4, 2), (2, −3) 6) (5, 9), (−1, 9)
7) (−7, 8), (−2, −9) 8) (2, −11), (−9, 0)
9) (4, −1), (2, −7) 10) (−4, −6), (3, −6)
11) (14, 0), (−7, 5) 12) (14, −8), (12, −1)
13) (−4, 12), (−7, −2)

14. Given the midpoint and one endpoint of a line segment, find the other endpoint.
1) Endpoint:(−9, −1), midpoint:(8, 14)
2) Endpoint:(10, 12), midpoint:(6, 9)
3) Endpoint:(−8, −10), midpoint:(10, −7)
4) Endpoint:(−11, 9), midpoint:(3, −11)
5) Endpoint:(−2, 7), midpoint:(12, −10)
6) Endpoint:(11, 14), midpoint:(10, 14)
7) Endpoint:(14, −8), midpoint:(5, 8)
8) Endpoint:(−9, 0), midpoint:(10, −7)