Question 1
Use matrix multiplication to move a triangle with vertices A(10,20) B(30,80) and C(70,0) to the right 50 pixels and down 30 pixels. What is the location of the new triangle?
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A'(60,50) B'(80,110) C'(80,-30)
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A'(-40,50) B'(-20,110) C'(20,-30)
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A'(60,-10) B'(80,50) C'(120,-30)
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A'(-40,-10) B'(-20,50) C'(-20,-30)
Question 2
For 3D translation by multiplication, the translation matrix looks like:
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![](data:image/png;base64, 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)
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