Find the 3 × 3 Matrix That Produces the Described $\left[ \begin{array} { c c c } 0.3 & - 0.4 \sqrt { 2 } & 0 \\ 0.3 \sqrt { 2 } & 0.4 & 0 \\ 0 & 0 & 1 \end{array} \right]$

question 78

Multiple Choice

Find the 3 × 3 matrix that produces the described composite 2D transformation, using homogeneous coordinates.
-Rotate points through 45° and then scale the x-coordinate by 0.6 and the y-coordinate by 0.8.

• A)
• \(\left[ \begin{array} { c c c } 0.3 & - 0.4 \sqrt { 2 } & 0 \\ 0.3 \sqrt { 2 } & 0.4 & 0 \\ 0 & 0 & 1 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { c c c } 0.3 \sqrt { 2 } & 0.3 \sqrt { 2 } & 0 \\ - 0.4 \sqrt { 2 } & 0.4 \sqrt { 2 } & 0 \\ 0 & 0 & 1 \end{array} \right]\)
• C)
• \[\left[ \begin{array} { c c c }
• 0.3 \sqrt { 2 } & - 0.3 \sqrt { 2 } & 0 \\
• 0.4 \sqrt { 2 } & 0.4 \sqrt { 2 } & 0 \\
• 0 & 0 & 1
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { c c c }
• 0 & - 0.6 & 0 \\
• 0.8 & 0 & 0 \\
• 0 & 0 & 1
• \end{array} \right]\]

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