Finding the distance between two points.

1
Finding the distance between two points.
(-4,4)
(4,-6)
2
Finding the distance between two points. Draw the
right triangle as shown.
(-4,4)
4-(-6)10
(4,-6)
(-4,-6)
3
Find the length of each leg.
(-4,4)
10
4-(-4)8
(-4,-6)
(4,-6)
4
Using the Pythagorean theorem, 102 82 D2,
we calculate the distance between the two
points. 10064 164 D2 . Thus D 164
(-4,4)
10
4-(-4)8
(4,-6)
(-4,-6)
5
To find a formula for this problem, we will
create the problem using variables.
(x2,y2)
(x1,y1)
6
To find a formula for this problem, we will
create the problem using variables.
(x2,y2)
D

(x2,y1)
(x1,y1)
x2 - x1
x2
x1

7
To find a formula for this problem, we will
create the problem using variables.
(x2,y2)
y2
D
y2 - y1
y1
(x2,y1)
(x1,y1)
x2 - x1
x2
x1
(x2 - x1)2 (y2 - y1)2
D2
8
The distance formula is
(x2 - x1)2 (y2 - y1)2
D
Find the distance between (-2,8) and (9, -5) D
(9 - (-2))2 (-5 - 8)2
9
The distance formula is
(x2 - x1)2 (y2 - y1)2
D
Find the distance between (-2,8) and (9, -5) D
(9 - (-2))2 (-5 - 8)2
D 112 (-13)2
10
The distance formula is
(x2 - x1)2 (y2 - y1)2
D
Find the distance between (-2,8) and (9, -5) D
(9 - (-2))2 (-5 - 8)2
D 112 (-13)2
D 121 169
11
The distance formula is
(x2 - x1)2 (y2 - y1)2
D
Find the distance between (-2,8) and (9, -5) D
(9 - (-2))2 (-5 - 8)2
D 112 (-13)2
D 121 169
D 290