Question

name pumpkin decoration transformations transform each figure as instructed below to decorate the pumpkins on your answer - sheet. each figure is numbered with the transformation that should be applied. 1 translate 23 units right 12 rotate 180 degrees around the origin 22 rotate 270 degrees clockwise around the origin 2 translate 19 units down 13 reflect over the x - axis 23 translate 17 units up and 4 units left 3 rotate 180 degrees around the origin 14 rotate 90 clockwise around the origin 24 reflect over the line x=-5 4 reflect over the x - axis 15 reflect over the y - axis 25 translate 3 units right and 22 units up 5 rotate 90 degrees counterclockwise around the origin 16 translate 2 units up 26 reflect over the x - axis and then translate 14 units down 6 translate 7 units down 17 reflect over the x - axis 27 translate 25 units up 7 rotate 180 degrees around the origin 18 rotate 180 degrees around the origin 28 reflect over the line x = 8 8 translate 8 units down 19 reflect over the x - axis 29 reflect over the line y=-2 9 translate 11 units right 20 reflect over the line y=-5 10 reflect over the x - axis 21 reflect over the y - axis and then reflect over the x - axis 11 reflect over the y - axis

Explanation:

Step1: Recall transformation rules

Translation: (x,y)→(x + a,y + b) for right - left (a) and up - down (b) shifts. Rotation 180° around origin: (x,y)→(-x,-y), 90° counter - clockwise: (x,y)→(-y,x), 270° clockwise: (x,y)→(y, - x). Reflection over x - axis: (x,y)→(x,-y), over y - axis: (x,y)→(-x,y), over line x = a: (x,y)→(2a - x,y), over line y = a: (x,y)→(x,2a - y).

Step2: Transform figure 1

For figure 1, translate 23 units right. If a point on figure 1 has coordinates (x,y), the new coordinates are (x + 23,y).

Step3: Transform figure 2

For figure 2, translate 19 units down. If a point has coordinates (x,y), the new coordinates are (x,y - 19).

Step4: Transform figure 3

For figure 3, rotate 180° around the origin. If a point has coordinates (x,y), the new coordinates are (-x,-y).

Step5: Continue for all figures

Apply the corresponding transformation rules to each of the 29 figures one by one following the above - mentioned rules for translation, rotation and reflection.

Since the actual drawing of the transformed figures on the answer sheet is required and cannot be fully represented in text, the general method to solve this problem is as described above. Each figure's transformation is based on the coordinate - based transformation rules for geometric figures.

Answer:

The transformed figures should be drawn on the answer sheet according to the rules: translations (add/subtract values to x or y coordinates), rotations (use specific coordinate - change formulas based on angle and center of rotation) and reflections (use appropriate coordinate - change formulas based on the line of reflection) for each of the 29 numbered figures.