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## 2-26-13 Transformations

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**2-26-13 Transformations**When and where might someone need to have an understanding of transformations? Is there a profession that uses transformations?**Check page 745 #1-24**For problems 1-6 You should have given properties to justify each step: Commutative property of addition Additive inverse Associative Property etc. 2(X+1) = 22 OPEN SENTENCE TRUE 45+5 = -50 FALSE 20 60 96 3b+25 3a-6c 5q+2 -17y+38 -3M+39 -x+2 -15 7 -24 23 -67 -22**A TRANSFORMATION is when a figure or point is moved to a new**position in a coordinate plane. This move may include a change in size as well as position. (Yesterday we worked with dilations which moved points in the plane to enlarge or reduce while creating a similar figure. This was a type of transformation.) A RIGID TRANSFORMATION is when the size and shape remain the same but the figure moves into a new position. Take a moment to add these two descriptions to your vocabulary.**There are four types of movement (TRANSFORMATIONS):**• DILATION…(Enlarges or Reduces) • TRANSLATION……(Slide) • REFLECTION……..(Flip) • ROTATION…….…..(Turn)**Today we will work with**TRANSLATIONS Stop and do Translation Activity Once ACTIVITY is complete, we will come back to the powerpoint and add to our notes.**http://www.brightstorm.com/math/geometry/transformations/translations/**http://www.brightstorm.com/math/geometry/transformations/translations/**TRANSLATION is a movement of a figure that involves a slide**in the x or y direction on a coordinate plane. More than one move may take place. Here is what a translation may look like. Notice that the direction the triangle is pointing did not change.**You have discovered that there are two methods to perform a**“TRANSLATION”. Each will give you the new “prime points”.**METHOD 1:**From each point, conduct the move requested one point at a time and then draw in your new image. Example: Plot points A(-2, 3), B(-6, 3), and C(-2, 7). Translate the figure 8 units right and 5 units down. C STEP 1:Plot original points STEP 2:From each original point move 8 units right and 5 units down. STEP 3:Connect the new points. This is your image and the points are the “prime” points. B A A(-2,3) A’(6, -2) B(-6,3) B’(2, -2) C(-2,7) C’(6, 2) STEP 4: Now list the location of the new points as your “primes”.**METHOD 2:**A right/left move will affect the x coordinate and an up/down move will affect the y coordinate. You can just do the arithmetic to each part of the ordered pair (coordinates). Example: Plot points A(-2, 3), B(-6, 3), and C(-2, 7). If the figure is translated 8 units right and 5 units down, name the prime points. The 8 units right will add 8 to the x number in the coordinate set and the 5 units down will subtract 5 from the y x y A(-2,3) -2 + 8 = 6 and 3 – 5 = -2 A’(6, -2) B(-6,3) -6 + 8 = 2 and 3 – 5 = -2 B’(2, -2) C(-2,7) -2 + 8 = 6 and 7 – 5 = 2 C’(6, 2)**Take a few moments now to add facts to your vocabulary sheet**about TRANSLATIONS Handout Translations D100**Summary:**When and where might someone need to have an understanding of transformations? Is there a profession that uses transformations? Homework: Textbook page 745, #25-39; Handout “Translations Practice”