1. Distance and Midpoints Objective: (1)To find the distance between two points (2) To find the midpoint of a segment

2. Definitions Midpoint: The points halfway between the endpoints of a segment. Distance Formula: A formula used to find the distance between two points on a coordinate plane. Segment Bisector: A segment, line, or plane that intersects a segment at its midpoint.

3. Midpoint To find the midpoint along the number line, add both numbers and divide by 2. 4 08261012-2-4-6 ABCDEFGHIJ Find the midpoint of BH The coordinate of the midpoint is 2. E is the midpoint.

4. More Midpoint For the midpoint on a coordinate plane, the formula is: B(-1,7) A(-8,1) This is the midpoint.

5. Finding the endpoint of a segment We’re still going to use the Midpoint Formula: But the there will be a few unknowns : Find the coordinates for X if M(5,-1) is the midpoint and the other endpoint has coordinates Y(8,-3) helps us find the x-coordinate of the endpoint.

6. Finding the endpoint of a segment Multiply both sides by 2 to eliminate the denominator -8 Subtract 8 from both sides x 2 = 2 This is the x-coordinate of the other endpoint This helps us find the y-coordinate of the midpoint

7. Finding the endpoint of a segment +3 y 2 = 1 This is the y-coordinate of the endpoint The coordinate of the other endpoint is X(2,1).

8. Finding the value of a variable M is the midpoint of AB. Find the value of x: Since M is a midpoint, that means that AM=MB which means 3x – 5 = x + 9 -x 2x – 5 = 9 +5 +5 2x = 14    A M B 3x - 5 x + 9 2x = 14 2 x = 7

9. Distance Remember: AB means the length of AB To find the distance on the number line, take the absolute value of the difference of the coordinates.  a – b  08261012-2-4-64 ABCDEFGHIJ Find CJ  -2 -12  =  -14  = 14 CJ = 14 Find EA  2 – (-6)  =  2+6  =8=8 = 8 EA = 8

10. More Distance The distance between two points in the coordinate plane is found by using the following formula: A(-3,1) B(4,-2)