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Published byCori Marsh Modified over 9 years ago
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Honors Geometry
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We learned how to set up a polygon / vertex matrix We learned how to add matrices We learned how to multiply matrices
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I will learn how to use matrices to model transformations.
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We use matrix addition to translate a figure We must set up the two matrices ourselves Polygon matrix Translation matrix Review rule for matrix addition
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This matrix will be added to the polygon matrix, so they must be the same dimension Once dimension is set, the top row of the matrix will reflect the horizontal shift of the translation, vertical on the bottom if left, negative, if right, positive This is the information from the translation vector
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Set up a translation matrix that will shift a triangle 4 units right and 2 units down Triangle: 2 x 3 Translation matrix:
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Shift the triangle ABC with vertices A(2, 4) B(4, 1) C(3, -3) along the vector Polygon matrix: Translation matrix: Add! A’ B’ C’
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Quadrilateral EFGH with vertices E(-3, 2), F(-2, 4) G(4, 1) H(3, 0) is translated 1 unit left and 3 units down. Write a translation matrix Find the coordinates of E’F’G’H’ E’(-4, -1) F’(-3, 1) G’(3, -2) H(2, -3) Graph the image and the preimage
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Graph both
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Both rotations and reflections use matrix multiplication We use a special set of 2 x 2 matrices to perform specific rotations and reflections Review rule for matrix multiplication Why will it always be possible to multiply a polygon matrix by a 2 x 2 special matrix?
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Reflection (based on line of reflection) Rotation (based on angle of rotation) x axis origin y axis y = x 90° 180° 270° 360°
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Notice: reflection about the origin and 180 degree rotation have the same special matrix Why? What does a 360 degree rotation do? Why is its matrix “extra” special?
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When multiplying by one of our 8 special matrices, always put the special matrix on the left (first) Remember that matrix multiplication is NOT commutative AB ≠ BA
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Reflect triangle ABC with vertices A(-3, 1) B(1, 3) C(2, 0) across the x axis Our two matrices: Multiply! A’ B’ C’
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Triangle XYZ with vertices X(1, -3) Y(-4, 1) Z(-2, 5) is rotated 180 degrees about the origin Find the coordinates of X’Y’Z’ X’(-1, 3) Y’(4, -1) Z’(2, -5) Graph the image and the preimage
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Graph
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