1. Midpoint and Distance Formulas

2. Definition
The midpoint of a segment is the point that divides the segment into two congruent segments.

3. Midpoint Formula
The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints.

4. Finding a Midpoint
Find the midpoint between the endpoints (1, 7) & (3, -4).
Find the midpoint between the endpoints (2, 5) & (-3, 9)

5. Finding an Endpoint
If the midpoint of segment AB is (2, 3) and A is at (-1, 5), where is B located?
If the midpoint of segment CD is (0, -2) and D is at (3, 4), where is C located?

6. Distance Formula
The distance formula is used to compute the distance between two points in a coordinate plane. It is given by:

7. Finding the Distance
Find the distance between the points (1, 4) and (-2, 8).

8. Partitioning a line segment in 1-dimension
A ratio of a:b means we are partitioning the segment into “a+b” parts 1) find the length of the segment 2) Multiply by the scaler “a/(a+b)” 3) Add your answer to the first endpoint to determine the coordinate of the partition

9. Example:
The endpoints of segment PQ are -3 and 7. Find the coordinates of the point P that partitions the segment in the ratio 3:5

10. “Taxicab” Distance Formula
Find the taxicab distance between (-2, 8) & (1,4) by graphing.

11. Practice A2 WS