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TRANSLATIONS

TRANSLATIONS. LESSON 28. TRANSLATION. In the diagram above, corresponding points on the two figures are related. Suppose P is any point on the original figure and P’ is the corresponding point on the image figure. We say: P maps onto P’ We write: P P’. MAPPING RULES.

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TRANSLATIONS

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  1. TRANSLATIONS LESSON 28

  2. TRANSLATION In the diagram above, corresponding points on the two figures are related. Suppose P is any point on the original figure and P’ is the corresponding point on the image figure. We say: P maps onto P’ We write: P P’

  3. MAPPING RULES We often use a coordinate grid when we work with transformations. We use a mapping rule to describe how points and their images are related. A mapping rule tells you what to do to the coordinates of any point on the figure to determine the coordinates of tits image. Example of Mapping rule: (x, y) (x + 5, y - 2) It tells you to add 5 to the x-coordinate and to subtract 2 from the y-coordinate.

  4. MAPPING RULES FOR TRANSLATIONS The transformation (x,y) (x + h, y + k) represents a translation for all values of h and k. YOU NEED TO MEMORIZE THE MAPPING RULES!!!!

  5. PROPERTIES OF A TRANSLATION The image figure is congruent to the original figure and has the same orientation. Line segments that join matching points have the same length and are parallel.

  6. EXAMPLE 1 A triangle with vertices P(4,-4), Q(7,1), and R(2,2) is translated. The image triangle has vertices P’(-2,-1), Q’(1,4), and R’(-4,5). Determine the mapping rule for translations.

  7. SOLUTION Draw the two triangles on a coordinate grid. To go from P to P’, move 6 units left and 3 units up. The same movements are required to go from Q to Q’ and R to R’. Hence, we subtract 6 from the x-coordinates and add 3 to the y-coordinates. The mapping rule is: (x,y) (x - 6, y + 3)

  8. EXAMPLE 2 • A triangle has vertices J(1,3), K(-3,-2), and L(2,-1). • Graph triangle JKL and its image triangle J’K’L’, under the translation (x,y) (x + 3, y - 3) • On the same grid, graph the image of triangle J’K’L’ under the translation (x,y) (x + 6, y + 5). • Describe the result of these successive translations. Write a mapping rule to represent the two translations combined.

  9. SOLUTION • Draw triangle JKL on a coordiante grid. To apply the mapping rule (x,y) (x + 3, y - 3), we add 3 to the x-coordinates and subtract 3 from the y-coordinates of each vertex of triangle JKL. This moves it 3 units right and 3 units down to become triangle J’K’L. • To apply the mapping rule (x,y) (x + 6, y + 5) to the image, we add 6 to the x-coordinates and add 5 to the y-coordinates of each vertex of triangle J’K’L’. This moves it 6 units right and 5 units up to become triangles J’’K’’L’’. The coordinates of its vertices are J’’(10,5), K’’(6,0), and L’’(11,1). • The combined result is a translation 9 units right and 2 units up. The mapping rule for this translation is (x,y) (x + 9, y + 2).

  10. Class Work • Check solutions to Lesson 27 worksheet • Copy Notes to Lesson 28 • Complete Lesson 28 worksheet

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