This document discusses the Pythagorean theorem and how it relates to the distance formula. It states that in a right triangle, the hypotenuse squared is equal to the sum of the legs squared. It then shows how to derive the distance formula from the Pythagorean theorem, allowing you to calculate the distance between two points by taking the difference of their x-coordinates squared plus the difference of their y-coordinates squared.

1. 1.3
How do I apply Ruler and
segment addition postulates?
What is the connection
between Pythagorean
Theorem & Distance Formula?

2. Section 1-3

3. *
*In a right triangle:
*Legs - the sides that form the right angle
*Hypotenuse – the side opposite the right angle.
Leg
Leg
Hypotenuse

4. **In a right triangle:
(hypotenuse)2 = (leg)2 + (leg)2
If m C = 90°, then c2 = a2 + b2
C A
B
b
a
c

5. *
The length of the hypotenuse is 13.
2
169c 
13c 
2 2 2
( ) ( ) ( )hypotenuse leg leg 
2 2 2
5 12c  
2
25 144c  
2
169c 
12
5
c

6. A
B
The Distance Formula Is Derived
From The Pythagorean Formula

7. A (-4, 3)
B (8, -2)
Distance Formula
The distance between two points
with coordinates (x1, y1) and (x2,
y2) is given by:
2
12
2
12 )yy()xx(d 

8. A
B
The Distance Formula Is Derived
From The Pythagorean Formula
2
12
2
12 )yy()xx(d 
22
)3)2(())4(8( d
22
)5()12( d
169d
13d

9. Find the Distance Between the points.
(-2, 5) and (3, -1)
Let (x1, y1) = (-2, 5) and (x2, y2) = (3, -1)
Example 4