Explanation Given information: The vertices are [ 0 0 ] , [ 1 0 ] , [ 1 1 ] and [ 0 1 ] . Calculation: First take the vertex [ 0 0 ] and multiply with the transformation matrix [ 1 0 0 − 1 ] such that it reflects the matrix in x -axis as, [ 1 0 0 − 1 ] [ 0 0 ] = [ 1 ⋅ 0 + 0 ⋅ 0 0 ⋅ 0 − 1 ⋅ 0 ] = [ 0 0 ] Then the matrix remains same as [ 0 0 ] . The obtained matrix [ 0 0 ] can be shown in Figure 1. Now, reflect the above graph about x axis and the resulted graph isshown in Figure 2. Now, take the matrix [ 0 0 ] as shown in Figure 1and use c = 2 in the transformation matrix [ c 0 0 1 ] to expand the vertex in the direction of x axis as, [ 2 0 0 1 ] [ 0 0 ] = [ 0 0 ] After expansion, the matrix remains same as [ 0 0 ] . Now, take the matrix [ 0 0 ] as shown in Figure 1and use c = 1 in the shear matrix [ 1 c 0 1 ] . After shear as, the matrix is obtained as, [ 1 1 0 1 ] [ 0 0 ] = [ 1 ⋅ 0 + 1 ⋅ 0 0 ⋅ 0 + 1 ⋅ 0 ] = [ 0 0 ] The obtainedmatrix remains same as [ 0 0 ] . Now, take the next vertex [ 1 0 ] and multiply with the transformation matrix [ 1 0 0 − 1 ] such that it reflects the matrix in x -axis as, [ 1 0 0 − 1 ] [ 1 0 ] = [ 1 ⋅ 1 + 0 ⋅ 0 0 ⋅ 1 − 1 ⋅ 0 ] = [ 1 0 ] Then the matrix remains same as [ 1 0 ] . The obtained matrix [ 1 0 ] can be shown in Figure 3. Now, reflect the above graph about x axis and the resulted graph is same as the initial graph as shown in Figure 3. Now, take the matrix [ 1 0 ] and use c = 2 in the transformation [ c 0 0 1 ] to expand the vertex in the direction of x axis as, [ 2 0 0 1 ] [ 1 0 ] = [ 2 ⋅ 1 + 0 ⋅ 0 0 ⋅ 0 + 1 ⋅ 0 ] = [ 2 0 ] After expansion, the matrix [ 1 0 ] becomes [ 2 0 ] as shown in Figure 4. Now, take the vertex [ 1 0 ] and use c = 1 in the shear matrix [ 1 c 0 1 ] such that the vertex is sheared as, [ 1 1 0 1 ] [ 1 0 ] = [ 1 ⋅ 1 + 1 ⋅ 0 0 ⋅ 1 + 1 ⋅ 0 ] = [ 1 0 ] After shear, the vertex remains same as [ 1 0 ] shown in Figure 3. Now, take the next vertex [ 1 1 ] and multiply with the transformation matrix [ 1 0 0 − 1 ] such that it reflects the matrix in x -axis as, [ 1 0 0 − 1 ] [ 1 1 ] = [ 1 ⋅ 1 + 0 ⋅ 1 0 ⋅ 1 − 1 ⋅ 1 ] = [ 1 − 1 ] Then the matrix becomes [ 1 − 1 ]

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ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6, Problem 1P

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The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.

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Chapter 6, Problem 20T

Chapter 6, Problem 2P

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The effect of the transformations on the vertices [ 0 0 ] , [ 1 0 ] , [ 1 1 ] and [ 0 1 ] of a square by sketching the graphs of the transformed vertices.

Solution Summary: The author analyzes the effect of the transformations on the vertices of a square by sketching the graphs.

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To find:

The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.

Want to see the full answer?

Chapter 6 Solutions

The effect of the transformations on the vertices [ 0 0 ] , [ 1 0 ] , [ 1 1 ] and [ 0 1 ] of a square by sketching the graphs of the transformed vertices.

Solution Summary: The author analyzes the effect of the transformations on the vertices of a square by sketching the graphs.

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To find: The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.

Want to see the full answer?

Chapter 6 Solutions

To find:

The effect of the transformations on the vertices [00],[10],[11] and [01] of a square by sketching the graphs of the transformed vertices.