1. Midpoints and Other Points on Line Segments
Adapted from Walch Education

2. Key Concepts
A line segment is a part of a line that is noted by two endpoints, (x1, y1) and (x2, y2).
The length of a line segment can be found using the distance formula,
The midpoint of a line segment is the point on the segment that divides it into two equal parts.

3. Finding the midpoint of a line segment is like finding the average of the two endpoints.
The midpoint formula is used to find the midpoint of a line segment. The formula is

4. Finding the Point on a Line Segment with Any Given Ratio
Other points, such as a point that is one-fourth the distance from one endpoint of a segment, can be calculated in a similar way.
We will explore that in class. Can’t wait!
Finding the Point on a Line Segment with Any Given Ratio

5. Practice # 1
Calculate the midpoint of the line segment with endpoints (–2, 1) and (4, 10).

6. Midpoint formula; Substitute (–2, 1) and (4, 10).
Substitute the values of (x1, y1) and (x2, y2) into the midpoint formula.
Midpoint formula;
Substitute (–2, 1) and (4, 10).

7. Simplify
The midpoint of the segment with endpoints
(–2, 1) and (4, 10) is (1, 5.5).
How do we show mathematically that (1, 5.5)
is the midpoint of the line segment with endpoints (–2, 1) and (4, 10)?

8. Thanks for Watching !!!
~Ms. Dambreville