1. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Vocabulary
The distance between any two points (x1, y1) and (x2, y2) is
Distance
Formula
The midpoint of a line segment is the point on the segment that is equidistant from the endpoints.
Midpoint
The midpoint M of a line segment with endpoints A(x1, y1) and B(x2, y2) is
Midpoint
Formula

2. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Example 1
Find the distance between two points
Find the distance between (4, -3) and (-7, 2).
Distance Formula
Substitute.
Simplify.
The distance between the points is ______ units.

3. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Checkpoint. Complete the following exercises.
1. Find the distance between (2, -3) and (5, 1).

4. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Example 3
Find the midpoint of a line segment
Find the midpoint of the line segment with endpoints (-3, 7) and (-1, 11).
The midpoint of the line segment is (____, ____).

5. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Checkpoint. Find the midpoint of the line segment with the given endpoints.

6. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Checkpoint. Find the midpoint of the line segment with the given endpoints.

7. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint
Example 2
Find a missing coordinate
Find the distance between (5, a) and (9, 6) is
Distance Formula
Substitute.
Simplify.
The distance between the points is ______ units.

8. Apply the Distance/Midpoint
4.1
Apply the Distance/Midpoint