THE DISTANCE FORMULA
During this lesson, we will use the
Distance Formula to measure
distances on the coordinate plane.
DISTANCE FORMULA
THE DISTANCE FORMULA
Given the two points (x1, y1) and (x2, y2), the
distance between these points is given by the
formula:
 (X
2 + (Y -Y )2
–X
)
1
2
1
2
Recall: You pick
which point is
first, then
second.
The diagram below shows the relationship between
the Distance Formula and the coordinates of two
endpoints of a line segment.
A
L
E
R
T
!
 (X1 –X2)2 + (Y1-Y2)2
EXAMPLE: Finding the length of
a segment, given its endpoints
 (X
2 + (Y -Y )2
–X
)
1
2
1
2
Let’s Practice:
What is the distance between the points
(5, 6) and (– 12, 40) ?
Let’s Practice:
Find the lengths of the segments. Tell
whether any of the segments have the same
length. Use the Distance Formula.
A (-1,1)
B (4,3)
AB = ___
A (-1,1)
C (3,2)
AC = ___
A (-1,1)
D (2,-1)
AD = __
AB = 13; AC = 17; AD = 13
Now, it’s your turn…..
What is the distance between (–2, 7) and (4, 6)?
6.08
What is your answer? _________
What is the distance between (–1, 1) and (4, 3)?
13
What is your answer? _________
ALGEBRA CHALLENGE: If the distance from (x, 3) to
(4, 7) is 41 , what is the value of x?
9
What is your answer? _________
Final Checks for Understanding
1. Find the distance between the two points.
C (0,0)
D (5,2)
2. Use the Distance Formula to determine if
JK = KL.
J(3,-5); K(-1,2) ; L (-5,-5)
_________________________________
J (3,-5)
K (1,2)
JK=
K (1,2)
L (-5,-5)
KL=