For lines that are vertical (x,y) or horizontal (x,y) the length is easy to find
All you have to do is subtract the y-coordinates to find my length
R
(-5, 9)
M
(-2, 3)
( 7, 3)
E
All you have to do to find me is subtract the x-coordinates
V
( -5, -7)

To find the length of a nonvertical or nonhorizontal the distance formula is to be used:
A
(-2,2)
B
(3,-3) x
1 and x
2 are the xcoordinates of A and B (it doesn’t matter which one is x
1 and which one is x
2 so it could be –2–3 or 3–(-2)) y
1 and y
2 are the ycoordinates of A and B (it doesn’t matter which one is y
1 and which one is y
2 so it could be 2 –(-3) or (-3)–2)

Here are some helpful examples:
Find the length of MR
M
(-3,9)
Find the length of CD
D
(1,8)
2 (x
1
-x
2
) + (y
1
-y
2
)
2 (-3-2) + (9+2)
2 (-5) + (11)
25 + 121
2
146
MR = 146
2
2
R
(2,-2)
C
(-3,-8)
2 (x
1
-x
2
) + (y
1
-y
2
) 2
2 (-3-1) + (-8-8) 2
2 (-4) + (-16) 2
16 + 256
16
272
17
CD = 4 17

Now you try:
1.) Find GK
G (1,4)
K
(4,0)
2.) Find LM
(-2,1)
L
M
(1,-4)
4.) Find XY
X
(-3,5)
3.) Find NO
N
(-1,2)
O
(0,-3) Y
(4,-5)

1.)
2
(4-1) + (4-0)
2
2
3 + 4
2
9 + 16
25
GK = 5
3.)
2 (0 + 1) + (2 + 3) 2
2 1 + 5 2
NO =
1 + 25
26
2.)
LM =
2
(1 + 2) + (1 + 4)
2
2
(3) + (5)
2
9 + 25
34
4.)
XY =
2 (4 + 3) + ( 5 + 5) 2
2
7 + 10
2
49 + 100
149

Find the perimeter of triangle RAY
A
(-3,11)
R
(-3,-7)
Y
(6,-7)

First find RA and RY
RA = 11 –(-7) RY = 6-(-3)
RA = 18 RY = 9
Now find AY using the distance formula
Now to find the perimeter add all the lengths together:
9 + 18 + 9 5
The perimeter is:
27 + 9 5
2
(6 + 3) + (11 + 7)
2
2
9 + 18
2
81 + 324
405
81
9 5
5

•Did you know the distance formula came from the
Pythagorean therom?
• http://www.mathwarehouse.com/algebra/distance_for mula/interactive-distance-formula.php
This site lets you drag around the points and see the distance formula at work
•Some fun practice http://www.regentsprep.org/Regents/Math/distance/Pr acDistance.htm

“Interactive Distance Formula” Math Ware House.
<http://www.mathwarehouse.com/algebra/distance_formula/interacti ve-distance-formula.php>. 29 May 2008
Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for
Enjoyment and Challenge. Boston: McDougal Little, 1991
Stapel, Elizabeth. "The Distance Formula.“ Purplemath.
<http://www.purplemath.com/modules/distform.htm>. 29 May 2008
“Working With Distance.” 1999-2008. Oswego City School District Regents
Exam Prep Center.
<http://www.regentsprep.org/Regents/Math/distance/PracDistance.ht
m>. 29 May 2008.