Power point on Distance Formula

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