2D Scaling Symmetric Scaling ·(12 pts) Given the square below with the listed vertices, first formulate a transformation matrix that scales it to make two times larger in both dimensions. Next apply the transformation matrix to each vertex. Show the new position of each vertex. ·(12 pts) Again, take the square vertices listed below and apply a formulated transformation matrix to scale it by 0.5 in the x-direction and by 0.2 in the y-direction. Show the new position of each vertex. Then apply a simple inverse matrix to undo the scaling that will return the square back to its original vertices. Show the position of the vertices after the transformation has been applied as well. ·(12 pts) Take a triangle with the below listed vertices and create a transformation matrix that will rotate it 180 degrees in the counter-clockwise direction. Next, apply the transformation matrix to each triangle vertex. List each vertex’s new position. Then, apply a simple inverse that will rotate it back to its original position. Show the position of the vertices after the transformation has been applied as well. ·(14 pts) For a square whose vertices are listed as below, form a composite matrix that will translate it to the origin, rotate it by 180 degrees counter-clockwise, and then translate it back to its original position. These transformations should be set up in a composite matrix. You should consider the translation of the square back to its original position as the simple inverse of the matrix that moved the square from its original position to the origin. Apply the composite matrix to each of the vertices listed below and then finally list each vertex’s final (x,y) coordinate value. Show the position of the vertices after the transformation has been applied as well, verifying that each vertex has been rotated by 180 degrees.
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