Find the distance between two points

1. Distance Formula
The student will be able to (I can):
• Find the distance between two points.

2. Pythagorean
Theorem
In a right triangle, the sum of the squares
of the lengths of the legs is equal to the
square of the length of the hypotenuse.
2 2 2 22 2
or b c b(ca a )+ = = +
y
x
a
b
c
●
●
a
22 2
c ba= +
22
c ba= +
22
164 93= + = +
25 5= =
●

3. distance
formula
Given two points (x1, y1) and (x2, y2), the
distance between them is given by
Example: Use the Distance Formula to find
the distance between F(3, 2) and G(-3, -1)
( ) ( )
2
1
2
2 2 1d xx y y= − + −
x1 y1 x2 y2
3 2 —3 —13 2 —3 —1
( ) ( )2 2
FG 3 3 1 2= − − + − −
( ) ( )2 2
6 3 36 9= − + − = +
45 6.7= ≈
Note: Remember that the square of a
negative number is positivepositivepositivepositive.

4. Problems 1. Find the distance between (9, —1) and
(6, 3).
A. 5
B. 25
C. 7
D. 13
( ) ( )( )
22
d 6 9 3 1= − + − −
( )2 2
3 4 25 5= − + = =

5. Problems 2. Point R is at (10, 15) and point S is at
(6, 20). What is the distance RS?
A. 1
B.
C. 41
D. 6.5
41
( ) ( )2 2
d 6 10 20 15= − + −
( )2 2
4 5 41= − + =