The Distance Formula

1
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 isnt horizontal or
vertical?You cant count blocks!
?
?
D(3, 2)
C(-2, -1)
4
Lets use our geoboards to model this situation.
We can form a right triangle with the segment CD
as the hypotenuse.
D
C
5
Lets use the Pythagorean Theorem to find the
length of segment CD.
D
3 units
C
5 units
a2 b2 c2 52 32 c2 25 9 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
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!!