1. Distance and Midpoint Formulas
Red Book
Lesson 4.1

2. EQ: How do you find the distance between two points
EQ: How do you find the distance between two points? How do you find the midpoint of a segment?

3. Vocabulary The Distance Formula
The distance d between any two points (x1, y1) and (x2, y2) is
d = √(x2 – x1)2 + (y2 – y1)2

4. Example 1 What is the distance between the points (3, 4) and (0, 0)?
First, label your original points:
x1 = 3, y1 = 4, x2 = 0, y2 = 0
Next, Plug and Chug:
d = √(0 – 3)2 + (0 – 4)2 = √ = √25
So the distance between the points is d = 5

5. The point equidistant from the endpoints of a line segment is called the midpoint.
A midpoint divides a line segment into two congruent segments (equal parts).

6. x-coordinates and the average (mean) of the y-coordinates.
The Midpoint Formula: The midpoint of a segment with endpoints (x1 , y1) and (x2 , y2) has coordinates
When you are finding the coordinates of the midpoint of a segment, you are actually finding the average (mean) of the
x-coordinates and the average (mean) of the y-coordinates.
The Midpoint Formula works for all line segments:  vertical, horizontal or diagonal.

7. Example 2
Find the midpoint of the segment with endpoints (3, 4) and (0, 0).
First, label your original coordinates:
x1 = 3, y1 = 4, x2 = 0, y2 = 0
Next, Plug and Chug:
((3+0)/2, (4 + 0)/2)
So the coordinates of the midpoint are (3/2, 2)