Chapter 1.2Distance Formula and Translations

04/21/23

D (3,5)

F(7,2)

B(3,2)

Look Familiar???

D (3,5)

F(7,2)B(3,2)

4

3?

Formula:

2 22 1 2 1( ) ( )d x x y y

Distance formula:

d = ( )2 + ( )2

04/21/23

11.31

Find the distance between the points P(-2, -5) and Q (-10, 3).

1, 1( )x y 2, 2( )x y

2 22 1 2 1( ) ( )d x x y y

2 53

8

d 64

65 d

-10

-8

64

128

d = ( )2 + ( )2

d = ( )2 + ( )2

Find the distance between the points P(-3, 2) and Q (-2, 4).1, 1( )x y 2, 2( )x y

2 22 1 2 1( ) ( )d x x y y

2 3 24

1 2

d 1 4

5 d 2.24

Do powers before doing the addition!!!!!!

Work inside parentheses

d = ( )2 + ( )2

d = ( )2 + ( )2

Geometry Transformations

A transformation is the mapping, or movement, of all the points of a figure in a plane according to a common operation.

A rigid motion is a transformation of points in space.

4/15/2011

Translation A transformation slides points the same

distance and in the same direction

The original figure is called the pre-image. The new figure created from the translation iscalled the image.

pre-image

image

Line segment PJ is horizontally translated (-10,0)

Then Translate P’J’ (0,-8)

How far would P”J” need to translate back to starting position?

P

J

P’

J’

(2,3)

(8,10)

(-8,3)

(-2,10)

(-8,-5)

(-2,2)

(10, -5) (-8, -3)

Try It On Your Own