Question

You may use a calculator and/or computer to carry out calculations. However you must show a sufficient amount of work to clearly communicate your solution to the reader. [A] Consider the L-shaped polygon with vertices: (-1,0), (1,0), (1,1), (0,1), (0,3), and (-1,3) shown to the right. Find the standard matrix for each of the transformations described below. Then use matrix multiplication to obtain the coordinates for the 6 vertices that result from applying the transformation to the vertices of the given rectangle. You may represent these 6 points as columns of a matrix when you write your answers. Finally, sketch the resulting polygon. on the attached answer sheet (last page)*** *Place your final answers to this problem (A.1) Rotation 90° counterclockwise about the origin. (A.2) Contract by a factor of 0.5, then project onto the line y x. (A.3) Shear by a factor of 1 (i.e. k 1) in the x-direction, reflect in the x-axis, then rotate 180° counterclockwise about the origin. Answer Sheet for Problem [A] (A.1) Standard Matrix Transformed Points: (matrix form is ok) (A.2) Standard Matrix = Transformed Points: (matrix form is ok) (A.3) Standard Matrix Transformed Points (matrix form is ok)

Answer 1

***Place your final answers to this problem on the attached answer sheet (last page)*** (A.1) Rotation 90° counterclockwise about the origin. (A.2) Contract by a factor of 0.5, then project onto the line y x. (A.3) Shear by a factor of 1 (i.e. k = 1) in the x-direction, reflect in the x-axis, then rotate 180° counterclockwise about the origin.

Answer Sheet for Problem [A] A B A be the standard (A.1) Standard Matrix= matsix then S o A 4 B A be the standand 4 (A.2) Standard matsix then Matrix= A 4 4 4T

tB A be the standand A (A.3) Standard Matrix= matsuix then - ) A

You may use a calculator and/or computer to carry out calculations. However you must show a sufficient amount of work to clearly communicate your solution to the reader. [A] Consider the L-shaped polygon with vertices: (-1,0), (1,0), (1,1), (0,1), (0,3), and (-1,3) shown to the right Find the standard matrix for each of the transformations described below. Then use matrix multiplication to obtain the Coordinates for the 6 vertices that result from applying the transformation to the vertices of the given rectangle. You may represent these 6 points as columns of a matrix when you write your answers. Finally, sketch the resulting polygon. (A 1) - [

3 A A 3 Points

(A-2) RIR - -N 1

the tansor mud points So asre taking bex) Iunit

A-3 A A A A

So thak taansforned points