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9.1 Translate Figure and Use Vectors

9.1 Translate Figure and Use Vectors. Translations http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/translation.swf&w=894&h=762&col=%23FFFFFF&title=Geometry+Translation Vector/Translations http://illuminations.nctm.org/LessonDetail.aspx?id=L474

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9.1 Translate Figure and Use Vectors

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  1. 9.1 Translate Figure and Use Vectors Translations http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/translation.swf&w=894&h=762&col=%23FFFFFF&title=Geometry+Translation Vector/Translations http://illuminations.nctm.org/LessonDetail.aspx?id=L474 Rotationshttp://illuminations.nctm.org/LessonDetail.aspx?ID=L466# rotational symmetryhttp://illuminations.nctm.org/LessonDetail.aspx?ID=L468

  2. Translation A translation moves a figure to a new location. • same shape • same size

  3. For all Transformations (including Translations) New figure is called an _____________. Original figure is called a _____________. image pre-image

  4. Translate a figure in the coordinate plane Example 1:Graph quadrilateral ABCD with vertices A(-1, 2), B(-1, 5), C(4, 6), and D(4, 3). Find the image of each vertex after the translation (x, y) → (x + 3, y – 1). Then graph the image using prime notation.

  5. are all Isometries If a transformation is an Isometry, then the image is the same shape and size of it’s pre-image. Types of Transformations (Preview- DON’T Write down) • Translation • Reflection • Rotation • Dilation

  6. Write a translation rule and verify congruence Write a rule for the transformations of ∆ ABC to ∆ A’B’C’. Then verify whether or not each transformation is an isometry. If so, use a congruence postulate (SAS, ASA, SSS, AAS). a) b)

  7. VECTORS • A vector is a quantity that has both _______________ and ______________________, or size. • It is used as another way to describe a _______________________________. • A vector is represented in the coordinate plane by an _______________ drawn from one point to another. direction magnitude translation ray

  8. F G 5,3

  9. Identify vector components Example 3: Name the vector and write its component form. 5, -2 -7, 0

  10. EXAMPLE 4: The vertices of ∆ABC are A(0, 3), B(2, 4), and C(1, 0). Translate ∆ABC using the vector 5,-1 .

  11. Example 5: The vertices of ∆ABC are A(-1, -1), B(0, 2), and C(1, 0). Translate ∆ABC using the vector .

  12. Translation Rule Another way of describing a translation on a coordinate plane. For example…. An image of shape translated by the vector 3, -2 would have the same image of a shape translated by (x,y)  (x+3, y-2).

  13. SUMMARY:Describing a Translation There are several ways to indicate that a translation is to occur: • Explain the translation from ABCD to A’B’C’D’ in words. • 2. Write the translation rule of ABCD to A’B’C’D’ in vector form. • 3. Write the translation rule for the translation ABCD to A’B’C’D’. The pre-image is shifted to the left 7 units and down 3 units

  14. Lets check! • http://regentsprep.org/regents/math/geometry/GT2/PracT.htm

  15. Let’s check your understanding http://regentsprep.org/regents/math/geometry/GT2/PracTran.htm

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