TRANSLATIONS AND VECTORS (OH YEAH!)

7.4

Translations

4

2

-2

-4

-5 5

R' Q'

P'

R Q

P

A transformation that maps every two points P and Q in the plane to points P’ and Q’ so that PP’ = QQ’ and PP’ is parallel to QQ’

Translation Facts

A translation does not affect the measurements

A translation does not affect the orientation.

That means it is an Isometry

That means that it stays exactly the same

Notation

We describe translations by showing the change in x and the change in y as addition or subtraction.

The notation x-5 shows that we have subtracted 5 from the original x value or we have moved 5 units to the left.

4

2

-2

-4

-5 5

-2

-5

(x-5,y-2)

(x,y)

Can you do it?

I have a triangle with points A(2,0), B(-2,-3) and C (4,-1)

If I translate by the rule (x+2,y-1), where will the new points be?

Hint: add 2 to all x values and subtract 1 from all y values

Answer: A’ (4,-1) B’ (0, -4) C’ (6,-2)

A double reflection over parallel lines is the same as a translation!!

The distance between preimage and image is twice the distance between the parallel lines.

Vectors

Vectors

A vector is a quantity that has both direction and magnitude

Physics Applications Force Velocity

Math application

Translations can be represented with vectors

A translation of a figure from one place to another is typically done in one direction with some amount of magnitude.

Example 1: Graphing Vectors -- Drag Strip. Discovery Education. 2007.Discovery Education. 24 February 2010<http://streaming.discoveryeducation.com/>

Vocabulary Terms

Initial Point: The beginning point of a vector (what the video called the tail)

Terminal Point: The ending point of a vector (what the video called the tip)

Component notation: replaces the translation notation of (x,y)(x+2,y-1) with

Comparison

Can be described as (x,y) (x+4,y+3)

Can also be describes as

4

2

-2

-4

-5 5

3 units

4 units

<4,3>

Can you do it?

Describe the transformation in both coordinate notation and component notation

Name the vector, give its component form, and find its magnitude.

Can you do it?

Consider the transformation

(x,y) (x-5, y+8)

Use a straight edge and graph paper to perform the transformation.

1. (x,y) (x+2,y-3)

2. <-2,4>

Exit TicketHomework

Using midpoints Using ReflectionsPG. 425: 15-32, 39, 40