Properties or Rules of Transformations

Equations used to find new locations

Translation

What do youNotice about thisTranslation goingFrom blue to red?How are the Ordered pairsAffected?

Translation

Basic Translation(x,y) (x+3,y)

Move each point 3 units right on the x axisCould rules for x, y or bothAdd to the x moves rightSubtract from x moves leftAdd to y moves upSubtract from y moves down

Reflection

3 typesOver the x axisOver the y axisOver the line y=x

Example

Given the following picture reflect over the y axis and the write the coordinates

Reflections

What do you think will happen with the x axis reflection? (x,y) (x,-y)Reflecting about the line y=x?(x ,y)(y,x)

4

2

-2

-4

-10 -5 5 10

This is reflection along the line y=x, notice the location of the original points and how they are different in the new image, x and y are reversed

Point (-1,2)Point (-4,1)Point (-3,5)

Point (2,-1)Point (1,-4)Point (5,-3)

Rotation about Origin

Rotate a figure 180 degrees about the origin what do you notice

Rotate a figure 90 degrees clockwise or counter clockwise what do you notice?

Old NewX Y X’ Y’2 3 -2 -35 1 -5 -14 6 -4 -6

Rule(x,y)(-x,-y)

Old NewX Y X’ Y’2 3 3 -25 1 1 -54 6 6 -4

Rule(x,y)(y,-x)

Coordinate Transformation

Reflect across y-axis the rule (x,y) (-x,y)Reflect across x-axis the rule (x,y)(x,-y)Reflect across y=x the rule (x,y)(y,x) Rotate about the origin 180 degrees the rule (x,y) (-x,-y)Translation about x-axis (x,y)(x+ or - #,y)Translation about y-axis (x,y)(x,y+ or - #)

Homework

Pg 380 1-8