Transformations

By: Mrs. Fischer

Learning Targets: 8.G.2,8.G.3, 8.G.4

Follow the slides to learn more about transformations

• Students should have paper and a pencil for notes at their desk while going through this presentation.

• Transformation: a transformation is a change in position, shape or size.

• The NEW figure you create after a transformation is known as the….? ________

• ______Notation is uses a tick mark to indicate the new image. If Triangle ABC is the original an A’B’C’ is the new image.

TRANSFORMATIONS

ANSWERS TO THE FILL IN

IMAGE and PRIME!!

There are 4 types of transformations

• REFLECTIONS or FLIPS

• TRANSLATIONS or SLIDES

• ROTATIONS or TURNS

• DILATIONS: Enlargement or Reduction of a pre-image.

Rigid

• Rigid Transformations are: reflections, rotations and translation.

• The transformation DOES NOT alter the size/shape of the figure.

Non Rigid

• Dilations are NON RIGID because this transformation alters the size/shape/orientation. A DILATION is a SHRINK or a STRETCH

Translations

• In a translation, Every POINT is moved the SAME distance and direction.

EX……

Translation Rules can be written in 3 different ways….

1 description 7 units to the left and 3 units down.(A verbal description of the translation is given.)

2.

mapping:

(This is read: "the x and y coordinates will be translated into x-7 and y-3". Notice that adding a negative value (subtraction), moves the image left and/or down, while adding a positive value moves the image right and/or up.)

3 notation:(The -7 tells you to subtract 7 from all of your x-coordinates, while the -3 tells you to subtract 3 from all of your y-coordinates.)This may also be seen as (x,y) = (x -7,y - 3).

Translation Rules

• Rules can be written to move a point. For example: (x,y) (x-6, y+1) indicates I would translate the pre-image 6 units to the left along the X AXIS and up 1 unit on the Y AXIS.

• Q 1.Write a rule (in each of the three formats) that would move a point 4 to the right and 5 units down.

Graph the given point

• Q2- If point A is located at (4,6), and you translated the figure to the left 3 units and down 2 units, What is the location of the new point?

• Q3-If point C located at (-5,2) was translated 9 units to the right and up one unit the new location of the point would be (-4,11)…is this TRUE OR FALSE? Explain.

• Q. 4 If you begin at 35 degrees latitude and 120 degrees longitude what translation rule will get you to 40 degrees latitude and 80 degrees longitude?

• What state did you begin at?• What state did you end at?

Click the DUDE to test YOUR Translation SKILLS

GOOD LUCK…… Do questions 1,3,5,7,9 and 13

REFLECTIONS

Navigate to the Brightstorm website by clicking the STAR below and watch the brief video on Reflection Transformations (you may take notes if you wish..if you need extra practice you may click on the other problem websites after watching the concept video.).

IF YOU DO NOT WANT TO SIGN UP FOR THE FREE ACCESS WITH YOUR EMAIL YOU CAN VISIT A SIMILAR VIDEO AT:

http://virtualnerd.com/pre-algebra/geometry/transformations-symmetry/reflecting-figures/reflect-y-axis-using-coordinates

• Rotational symmetry is when the shape or image can be rotated and still look the same.

• Click to interactively investigate Rotations. (Work through mathewarehouse on the computer)

• Click to learn about the ANGLE of ROTATION (read through ALL the slides) You should be able

to answer questions such as: what is the angle of rotation of an equilateral triangle? Of a regular hexagon? Of a rectangle? You do not have to record anything for this slide.

ROTATIONAL SYMMETRY

DILATIONS

• A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure.

OBSERVE: Notice how EVERY coordinate of the original pentagon has been multiplied by the scale factor (1/3).

Dilation CONTINUED>

OBSERVE: Point E and its image are the same. It is important to observe the distance from the center of the dilation, E, to the other points of the figure. Notice EF = 6 and E'F' = 3.

To the left the pre-image of rectangle EFGH with the center of dilation at point E and a scale factor of ½ yields E’F’G’H’.

YOU MADE IT.

• WOOHOO!