The document explains the distance formula and how to calculate the distance between two points in a coordinate plane. It provides the formula for distance as the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points. Several examples are given of using the distance formula to calculate the distance between points with given coordinates.

1. The Distance
Formula
3102.4.3 Understand horizontal/vertical distance in a
coordinate system as absolute value of the difference
between coordinates; develop the distance formula for a
coordinate plane using the Pythagorean Theorem.

2. The Distance Formula
The distance d between any two
points with the coordinates
(x1,y1) and (x2,y2) is given by
2 2
2 1 2 1( ) ( )d x x y y= − + −
A (x1,y1)
B (x2,y2)

3. Distance Between Two Points
Find the distance between the points at
(2,3) and (-4,6)
2 2
2 1 2 1( ) ( )d x x y y= − + −
2 2
( 4 2) (6 3)= − − + −
Now just type this into your calculator!
Round your
answer
6.71

4. Try this one!
Find the distance between (1,2) and (-3,0)
Answer is 4.47

5. Find the distance using the
Pythagorean Theorem!
7
5
a2
+b2
=c2
(5)2
+(7)2
=c2
25 + 49 =c2
74 =c2

6. Now try these
(12,3) and (-8,3)
(6,8) and (3,4)
(0,0) and (5,12)
(-4,2) and (4,17)

7. Try this one using the
Pythagorean Theorem!