Lesson 1-3Section 1-5

Definition

Definition

To find the Midpoint of a number line, we simply take the average of the distance.

Say that we are trying to find the distance between two points, a and b. To take the average of these points we add a and b together and then divide it by 2. I.E. a+b/2

Questions

Example 1 will be done on the board.

We can also use the fact that the midpoint is in the middle and therefore cuts the segment in half. Let’s see what theorem 1-1 says about that.

Theorem 1-1 Midpoint Theorem

If M is the midpoint of AB, then AM ~= MB

Example 2

Example 3

Question

We saw what a midpoint looks like on a line, but what if we are trying to find the midpoint in a coordinate plane?

The coordinate plane has points (x,y). To find the middle of a segment we simply find the average of the distance between the endpoints. Let’s see how that is done…..

Definition

Example 4

Example 9

Example 10

Example 11

Practice

Try the following problems:

Pg. 40 # 7-13 odd