The Distance Formula

with Ed and Leslie

Pythagorean Theorem Review

• Pythagorean Theorem:– Right Triangles: a2 + b2 = c2

• Pythagoras – 569 BC – 475 BC

• Pythagorean Brotherhood Motto:– “All is Number”

• Hippasus discovered irrational numbers

c2

a2

b2

1

1

2

Horizontal Distance

(2 , 3) (11 , 3)

Hey Ed, How far apart are we?

Not far enough.

Just kidding. How should I know how far

apart we are?

Just count the spaces between us.Okay

1 2 3 4 5 6 8 97

It looks like we are 9

spaces apart.

That’s right! You could find that out by

subtracting our x coordinates.

11 2 9

That makes sense.

Horizontal Distance is the change in the x

direction.

Vertical Distance

(5 , 4)

(5 , 11)

123

4567

11 4 7 7, The distance between us is 7.

Ed, What is the distance between

us now?

Very Good, Ed. The vertical distance is the

difference in the y coordinates.

Let me count the spaces.Huh?

Hey, Ed come overUse the distance

formula.

How far is it?

How should I know?

What’s that?

Distance Formula

I can’t. It’s too far

No it’s not

Yes it is

2 2

2 1 2 1D x x y y

(2 , 1)

(8 , 9)

2 2

2 1 2 1

2 2

2 2

8 2 9 1

6 8

36 64

100

10

D x x y y

D

D

D

D

D

10

Here it comes

How do I use it?

Great, I will be (x2,y2). Then we just use the formula. Here

are my coordinates.

Just use our coordinates in the formula. You can be (x1,y1). What are your coordinates?

Distance Formula

(-4, 0) (4, 0)

(0, -3)

2 2

2 1 2 1D x x y y

Distance Formula & Pythagorean Theorem

(x1,y1)

(x2,y2)

2 2

2 1 2 1D x x y y

(x2-x1)

(y2-y1)D

2 2 2

2 2

c a b

c a b

= c= b

= a

Mathematical Psychic Mind Reader