This document discusses finding the distance between two points and finding the midpoint of a segment. It defines distance as being the same regardless of the order of the endpoints and can be found using the Pythagorean theorem or distance formulas. The midpoint of a segment is found by taking the average of the x-coordinates and y-coordinates of the two endpoints. Examples are provided to find the distance between two points on a number line and to find the midpoint of a segment given the endpoints' coordinates.

1. 1.3 Distance and Midpoints

2. Objective Find the distance between two points Find the midpoint of a segment

3. Distance between two points The coordinates of the endpoints of a segment can be used to find the length of the segment. Because the distance from A to B is the same as the distance from B to A, the order in which you name endpoints makes no difference.

4. Pythagorean Theorem

5. Distance Formulas Number line Coordinate Plane

6. Examples Use a number line to find CD. The coordinates of C and D are -6 and -3. Find the distance between E(-4,1) and F(3,-1).

7. Midpoint Number Line The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is Coordinate Plane The coordinates of the midpoint of a segment with endpoints that have coordinates and are

8. Examples The coordinates on a number line of J and K are -12 and 16, respectively. Find the coordinate of the midpoint. Find the coordinates of the midpoints of the coordinates G(8,-6) and H(-14,12)