Polygons and Transformations Unit 2

Essential Questions 1.) How can you change a figure’s position without changing its size and shape? 2.) What process is used to perform a reflection across a line?

What are Transformations? (Ch. 9.1) Definition: The methodical movement of a geometric figure on a plane. The starting figure is called a “pre-image” and the resulting figure is called an “image”. Characteristics and Tendencies: There are 4 types: Translation, Rotation, Reflection, and Dilation. Follows the same naming/labeling rules used with ≅ figures Translation, Rotation, and Reflection are called the Rigid Transformations. Example: ∆ABC → ∆A’B’C’ Non-Examples: ABCD → A’C’B’D’ Transformations

A Foldable for your Journal

The Top Flap III IIIIV (+,+) (-,+) (-,-)(+,-) X-Axis Left and Right - + Y-Axis Down and Up - + Coordinates (x,y) Pre-Image → Image A → A’ Original → Result Before → After

Problem 3 (pg 547)

T ( ∆PQR) Item Being Affected Translation Change of X Value Change of Y Value Could Also be represented as: (x-2, y-5) Left 2 and Down 5

Inside the top flap Summarize what is happening to the transformation in your own words!

What are Reflections? (Ch. 9.2) A reflection over a line k is a transformation in which each point of the original figure (pre- image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line. Remember that a reflection is a flip. When reflecting over the x axis, the sign of y changes When reflecting over the y axis, the sign of x changes The notation for reflections: r k The image keeps the same dimensions as the preimage

Lets take a look at an example 1.) Look at this problem and let’s go over it! (remember to put this cutout in your journal, not in your foldable)

R y-axis ( ABC) Reflection The line you are reflecting over The item being affected XYNew XNew Y A-34A’34 B01B’01 C42C’-42 Since we’re reflecting over the y-axis, only the X’s are affected

Now let’s go back to our foldable…. On the Inside of the 2 nd flap Summary: Vertical or Horizontal Axis: Count from each vertex of the pre-image to the axis of reflection and then count the same value again. y=x OR y=-x Switch the x and y values for each vertex in the pre-image. BOTH versions result in points that are equidistant from the axis of reflection.

F G H F’ H’ G’ On the Front of the Third Page From Pg 557 in Textbook R y-axis ( ∆FGH) Reflection Figure Effected Axis of Reflection Reflection (Flip) F G H F’ H’ G’ R y=-1 ( ∆FGH) F G H F’ H’ G’ R y=x ( ∆FGH) (2,2) (4,-3) (-2,-1) (-1,-2) (-3,4) (2,2)

Inside the top flap Summarize in your own words how to reflect an object! Now Let’s Practice!

On the Back of the Third Page Summary: Based on the required rotation to each vertex, determine the resulting Quadrant, switch the x and y values if necessary, and then apply the – and + values as appropriate.

On the Front of the Fourth Page From Pg 565 in Textbook r (90˚, O) ( ∆FGH) Figure Effected Rotation Degree of Rotation Center of Rotation (in this case it is origin) Rotation (Flip) 0˚=(x,y) 90˚=(y,x) 180˚=(x,y) 270˚=(y,x) 360˚=(x,y) Every Quadrant is a total of 90˚ F J H F’ H’ G’ QuadrantsIIIIIIIV (+,+) (-,+) (-,-)(+,-) Counter – Clockwise Positive Rotation Clockwise Negative Rotation G J’