1. Midpoint Formula

2. In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates ( x 1, y 1 ) and ( x 2, y 2 ) are:

3. Recall: The point on a line segment is the midpoint if it divides that line segment into two congruent line segments. A BM Since AM ≃ MB Then point M is the midpoint of AB

4. Visualizing with Coordinate Plane (2, 3)(8, 3) (5, 3) M

5. Using the Formula Find the midpoint between the the points (2, 3) and (8, 3) x 1 = 2 x 2 = 8 y 1 = 3 y 2 = 3 M = 2 + 8, 3 + 3 2 2 M = 5, 3

6. Example 1 Use both a coordinate plane and the midpoint formula to find the midpoint between the points (-4, 4) and (2, 4)

7. Visualizing with Coordinate Plane (-4, 4) (2, 4) (-1, 4) M

8. Using the Formula Find the midpoint between the the points (-4, 4) and (2, 4) x 1 = -4 x 2 = 2 y 1 = 4 y 2 = 4 M = -4 + 2, 4 + 4 2 2 M = -1, 4

9. Example 2 Use both a coordinate plane and the midpoint formula to find the midpoint between the points (3, 3) and (9, 7)

10. Visualizing with Coordinate Plane (3, 3) (9, 7) (6, 5) M

11. Using the Formula Find the midpoint between the the points (3, 3) and (9, 7) x 1 = 3 x 2 = 9 y 1 = 3 y 2 = 7 M = 3 + 9, 3 + 7 2 2 M = 6, 5

12. More Practice Find midpoint between the points (-4, 2) and (8, -6) Find the midpoint between (-2, 5) and (6, 4) Find the midpoint between (7, -2) and (-4, 8). A is the midpoint of FT. If F (6,4) and T (-6,-4) find A. Find the midpoint of BN if B (3.5,-2) and N (-7.5,11). XC is bisected by OP at E. If X (0,0) and C (12, 0) find E. (2, -2) (2, 9/5) (1.5, 3) (0, 0) (-2, 4.5) (6, 0)

13. Endpoint If you are given one endpoint and a midpoint, how can you find the other endpoint? M is the midpoint between points P and K. If M is (3,4) and P is (1, 3) what is K?

14. Two Solutions: M = (3, 4) and P = (1, 3) 3 = 1 + x 2 2 4 = 3 + y 2 2 K = (5, 5) P = (1, 3) M = (3, 4) When you go from 1 to 3 you added 2 thus add 2 to 3 When you go from 3 to 4 you added 1 thus add 1 to 4 K = (5, 5)

15. More Practice RO has a midpoint D. If R (3, 1) and D (11, 5) find O A line segment has an endpoint (1,1) and a midpoint (10, 10) find the other endpoint PO has a midpoint of (-1.5, 3). If P (2, -1) find O. (19, 9) (19, 19) (-5, 7)