1. Midpoint and Distance Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the Distance Between Two Points on a Coordinate Plane 12.6

2. The Midpoint Formula The midpoint between the two points (x 1, y 1 ) and (x 2, y 2 ) is:

3. Find the midpoint of the segment whose endpoints are (6,-2) & (2,-9) Example 1

4. Example 2 Find the coordinates of the midpoint of the segment whose endpoints are (5, 2) and ( 7, 8)

5. Example 3 Find the coordinates of the midpoint of the segment whose endpoints are (-2, 8) and ( 4, 0)

6. Distance Formula The distance between two points with coordinates (x 1, y 1 ) and (x 2, y 2 ) is given by:

7. Find the Distance Between the points. (-2, 5) and (3, -1) (-2, 5) and (3, -1) Let (x 1, y 1 ) = (-2, 5) and (x 2, y 2 ) = (3, -1) Let (x 1, y 1 ) = (-2, 5) and (x 2, y 2 ) = (3, -1) Example 4

8. Example 5 What is the distance between P(- 1, 4) and Q(2, - 3)?

9. Example 6 What is the distance between P(3, 0) and Q(5, - 4)?

10. Example 7 What is the distance between P(-5, 2) and Q(2, - 5)?

11. Example 8 Use the distance formula to determine whether the three points are vertices of a right triangle: (1,1), (4,4), (4,1)

12. Example 9 Use the distance formula to determine whether the three points are vertices of a right triangle: (3, -4), (-2, -1), (4, 6). p. 748 #16-28e, 36-44e, 61-63