1. Amy Hatfield Central High School
The Distance Formula
A(-4, 3)
B(8, -5)
Amy Hatfield
Central High School

2. Finding the length of vertical or horizontal segments in the coordinate plane is simple: just count the number of blocks from one endpoint to the other! A B X Y
AB = 8 units
XY = 7 units

3. What do you do if the segment isn’t horizontal or vertical
What do you do if the segment isn’t horizontal or vertical? You can’t count blocks! ? ?
D(3, 2)
C(-2, -1)

4. Let’s use our geoboards to model this situation
Let’s use our geoboards to model this situation. We can form a right triangle with the segment CD as the hypotenuse. D C

5. Let’s use the Pythagorean Theorem to find the length of segment CD.
3 units C
5 units
a2 + b2 = c2
= c2
= c2
c2 = 34
c =34  5.83 units

6. The number 5 came from the positive difference between the two x coordinates, x1 and x2.
Likewise, the number 3 came from the positive difference between the two y-coordinates, y1 and y2.
D(x2, y2)
C(x1, y1)

7. This is the distance formula!!
Now, using the Pythagorean Theorem, plug in the variables instead of the numbers.
c2 = a2 + b2
d2 = (x2 – x1)2 + (y2 - y1)2
d = (x2 – x1)2 + (y2 - y1)2
This is the distance formula!!