Question

Computer Graphics Refer to Problem 71. The points $(-3,0),(-1,-2),(3,1)$and $(1,3)$are the vertices of a parallelogram ABCD.

(a) Find the new vertices of a parallelogram role="math" localid="1646829357237" $A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$if it is translated by .

(b) Find the new vertices of a parallelogram $A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$ if it is translated by $-\frac{1}{2}v$.

Short answer

Step-by-step solution

Part (a) Step 1. Translation by V

$$\begin{gathered} {\mathbf{A}}^{\mathrm{\prime }}=\mathbf{A}+\mathbf{V} \\ =⟨-3,0⟩+⟨3,-2⟩=⟨0,-2⟩ \\ {\mathbf{B}}^{\mathbf{\prime }}\mathbf{=}\mathbf{B}\mathbf{+}\mathbf{V} \\ =⟨-1,-2⟩+⟨3,-2⟩=⟨2,-4⟩ \\ {\mathbf{C}}^{\mathbf{\prime }}\mathbf{=}\mathbf{C}\mathbf{+}\mathbf{V} \\ =⟨3,1⟩+⟨3,-2⟩=⟨6,-1⟩ \\ {\mathbf{D}}^{\mathbf{\prime }}\mathbf{=}\mathbf{D}\mathbf{+}\mathbf{V} \\ =⟨1,3⟩+⟨3,-2⟩=⟨4,1⟩ \end{gathered}$$

Part (b) Step 1. Translation by -12V