Transformations

TranslationReflectionRotationDilation

Transformation

Changing the position (location) or size of a figureWe will be focusing on 2 Dimensional figures on the coordinate plane

Translation

Moving a figure around the coordinate systemSliding it left, right, up or down, all the points (vertices) are moved the same

Problem 3.1

Problem 3.1 B,C and D

When you translate a figure all the parts are congruent, meaning the same as the original

Reflection

A transformation that flips an image over a line called the line of reflectionThink of a mirror image on the other side of a lineThe image has things backwardsWe are only going to do reflection over the x and y axis

Problem 3.2

A. When reflecting an image over a line the original image and the new image are the same distance from the line of reflection

B. The lines are opposite, the original is negative the reflection is positive

C. The images would be exactly on top of each otherDistances are the same to the line of reflectionTriangles are still congruent or the exact same

Rotation

Turns a figure around a fixed point, in this case the originWe are also only going to talk about rotations that are 90,180, or 270 degrees, but we may refer to a specific directionCenter of Rotation – origin or fixed point you are turning the figure aroundClockwise and Counterclockwise direction

Problem 3.3

Try to do the rotation and see if as a group you can come up with an explanation of how to do this

Problem 3.4

Vertex is not the center of rotation, it can be but isn’t always

Rules/Ideas for Transformations

Translate – moving each on the vertices the same L,R, up or down, could be one or two things for each point, figures are congruentReflection – mirror image over the x or y axis, find the distance the original vertex is from the line of reflection and move the same distance to the other side, do with all points and connectRotation – Write down the coordinates of the original figure, turn the paper until the quadrant the new figure will appear in is in the upper left (where quadrant 1 originally was) re-plot the points

Rules/Equations

If it is easier to apply an equation to each of the rulesTranslation – (x,y)(x+ #,y) right

(x,y)(x-#,y) left(x,y) (x,y+#) up(x,y) (x,y-#) Down

More

Reflection over y-axis(x,y)(-x,y)

Reflection over x-axis(x,y) (x,-y)

Rotation 180 about origin (doesn’t matter direction)(x,y)(-x,-y)

Rotation 90 clockwise about origin(x,y) (y,-x)

Rotation 90 counterclockwise(x,y)(-y,x)

Homework

Page 18 2,3,5,9Worksheets for translation, reflection, rotation