1. Finding the Midpoint
To discover the coordinates of the midpoint of a segment in terms of those of its endpoints
To use coordinates of the midpoint of a segment and knowledge of slope to write equations of lines in polygons

3. In the Middle
In this investigation you will discover a method for finding the coordinates of the midpoint of a segment. As you work through the steps, think about which algebra concepts help you find a midpoint.
Plot the points A(1, 2), B(5, 2), and C(5, 7) and connect them.
Find the midpoint of AB. How did you find this point?
Find the midpoint of BC. How did you find this point?
Find the midpoint of AC.
How does the midpoint’s x-coordinate compare to the x- coordinates of A and C?
How does its y-coordinate compare to the y-coordinates of A and C?

4. Example
Consider the points D(2, 5) and E(7, 11). Find the midpoint of
Explain how to find the coordinates of the midpoint of a line segment between any two points.
Find the midpoint of the segment between each pair of points.
a. F(7, 42) and G(2, 14)
b. H(2.4, 1.8) and J(4.4, 2.2)
Make a conjecture about a formula for the midpoint of the segment connecting
(a, b) and (c, d).

5. Example A triangle has vertices A(-4,3), B(5,9), and C(0,-3).
Write the equation of the median from vertex B.
Write the equation of the perpendicular bisector of AB.