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Mod9 les2 rot dil

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This document discusses rotations and dilations of geometric shapes. It defines a rotation as turning a shape around a center point, with all points maintaining their distance from the center. A dilation stretches or shrinks a shape by a scale factor, where a factor greater than 1 results in enlargement and between 0 and 1 results in shrinking. Examples are provided of rotating and dilating triangles, with step-by-step workings to find the new point coordinates. Additional online practice resources are recommended for mastering these transformation techniques.

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Transformations ROTATIONS AND DILATIONS
What is a rotation? Rotation means turning around a center The distance from the center to any point on the shape stays the same. Every point makes a circle around the center. Check out my source for a neat GIF that shows a rotation. Source: http://www.mathsisfun.com/geometry/rotation.html
Rotation Tricks If your original point A (x , y) is rotated 90属 counterclockwise it becomes A(-y , x). If your original point B (x, y) is rotated 90属 clockwise it becomes B(y, -x) If your original point C (x, y) is rotated 180属 counterclockwise or clockwise it becomes (-x, -y). (if you go 180属 in counterclockwise or clockwise they would both end up in the same place) If your original point D (x, y) is rotated 270属 counterclockwise it becomes D(y, -x). (Same as 90属 clockwise)
Try These Rotate Q (-1, 3) 90属 counterclockwise about the origin. Rotate M(4, -6) 270属 counterclockwise about the origin. Rotate N (-2, -3) 180属 clockwise about the origin. Rotate Triangle T (0, -9) U (7, 8) V (-6, 3) 90属 clockwise about the origin.
Answers. Q (-3, -1) M (-6, -4) N (2, 3) T(-9, 0) U(8, -7) V(3, 6) This is a great site that has more practice if you need it! It will really help you with the Mastery Assignment. http://www.ixl.com/math/geometry/rotations-find-the-coordinates
Dilations A dilation stretches or shrinks an object. It is the same shape as the original, just a different size. The scale factor is how much the object stretches or shrinks. If the scale factor is greater than one, the object stretches. If it between zero and 1 (0<k<1) then the object shrinks. To find the new image, simply multiply the points by the scale factor. Source: http://www.regentsprep.org/regents/math/geometry/gt3/ldilate2.htm
Try some Triangle A (-2, 3) B(3, 6) C (-5, 9) is dilated by a scale factor of 遜. Find the new points of the image. Triangle Q (4, -1) R (-4, 8) S (10, 2) is dilated by a scale factor of 3. Find the new points of the image. Triangle D (-3, -4) E (6, 8) F (12, 2) is dilated and is now at D (-6, -8) E (12, 16) F (24, 12). By what scale factor did the dilation occur?
Answers A (-1, 1.5) B (1.5, 3) C (-2.5, 4.5) Q (12, -3) R (-12, 24) S (30, 6) Scale factor = 2 Need some extra practice to get ready for the mastery assignment? http://www.ixl.com/math/grade-8/dilations-find-the-coordinates

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Mod9 les2 rot dil

  • 2. What is a rotation? Rotation means turning around a center The distance from the center to any point on the shape stays the same. Every point makes a circle around the center. Check out my source for a neat GIF that shows a rotation. Source: http://www.mathsisfun.com/geometry/rotation.html
  • 3. Rotation Tricks If your original point A (x , y) is rotated 90属 counterclockwise it becomes A(-y , x). If your original point B (x, y) is rotated 90属 clockwise it becomes B(y, -x) If your original point C (x, y) is rotated 180属 counterclockwise or clockwise it becomes (-x, -y). (if you go 180属 in counterclockwise or clockwise they would both end up in the same place) If your original point D (x, y) is rotated 270属 counterclockwise it becomes D(y, -x). (Same as 90属 clockwise)
  • 4. Try These Rotate Q (-1, 3) 90属 counterclockwise about the origin. Rotate M(4, -6) 270属 counterclockwise about the origin. Rotate N (-2, -3) 180属 clockwise about the origin. Rotate Triangle T (0, -9) U (7, 8) V (-6, 3) 90属 clockwise about the origin.
  • 5. Answers. Q (-3, -1) M (-6, -4) N (2, 3) T(-9, 0) U(8, -7) V(3, 6) This is a great site that has more practice if you need it! It will really help you with the Mastery Assignment. http://www.ixl.com/math/geometry/rotations-find-the-coordinates
  • 6. Dilations A dilation stretches or shrinks an object. It is the same shape as the original, just a different size. The scale factor is how much the object stretches or shrinks. If the scale factor is greater than one, the object stretches. If it between zero and 1 (0<k<1) then the object shrinks. To find the new image, simply multiply the points by the scale factor. Source: http://www.regentsprep.org/regents/math/geometry/gt3/ldilate2.htm
  • 7. Try some Triangle A (-2, 3) B(3, 6) C (-5, 9) is dilated by a scale factor of 遜. Find the new points of the image. Triangle Q (4, -1) R (-4, 8) S (10, 2) is dilated by a scale factor of 3. Find the new points of the image. Triangle D (-3, -4) E (6, 8) F (12, 2) is dilated and is now at D (-6, -8) E (12, 16) F (24, 12). By what scale factor did the dilation occur?
  • 8. Answers A (-1, 1.5) B (1.5, 3) C (-2.5, 4.5) Q (12, -3) R (-12, 24) S (30, 6) Scale factor = 2 Need some extra practice to get ready for the mastery assignment? http://www.ixl.com/math/grade-8/dilations-find-the-coordinates