Find the 3 × 3 matrix that produces the described transformation, using homogeneous coordinates.
-$( x , y ) \rightarrow ( x + 7 , y + 4 )$
A)
$\left[ \begin{array} { l l l } 7 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { l l l } 1 & 0 & 7 \ 0 & 1 & 4 \ 0 & 0 & 0 \end{array} \right]$

C)
$\left[ \begin{array} { l l l } 1 & 0 & 4 \ 0 & 1 & 7 \ 0 & 0 & 1 \end{array} \right]$

D)
$\left[ \begin{array} { l l l } 1 & 0 & 7 \ 0 & 1 & 4 \ 0 & 0 & 1 \end{array} \right]$

Question

Find the 3 × 3 matrix that produces the described transformation, using homogeneous coordinates.
-$( x , y ) \rightarrow ( x + 7 , y + 4 )$
A)
$\left[ \begin{array} { l l l } 7 & 0 & 0 \ 0 & 4 & 0 \ 0 & 0 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { l l l } 1 & 0 & 7 \ 0 & 1 & 4 \ 0 & 0 & 0 \end{array} \right]$

C)
$\left[ \begin{array} { l l l } 1 & 0 & 4 \ 0 & 1 & 7 \ 0 & 0 & 1 \end{array} \right]$

D)
$\left[ \begin{array} { l l l } 1 & 0 & 7 \ 0 & 1 & 4 \ 0 & 0 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The correct matrix for a translation transformation in homogeneous coordinates is $\left[ \begin{array} { l l l } 1 & 0 & \Delta x \ 0 & 1 & \Delta y \ 0 & 0 & 1 \end{array} \right]$, where $\Delta x$ and $\Delta y$ are the changes in the x and y directions, respectively. Here, $\Delta x = 7$ and $\Delta y = 4$, so the correct matrix is $\left[ \begin{array} { l l l } 1 & 0 & 7 \ 0 & 1 & 4 \ 0 & 0 & 1 \end{array} \right]$.

Find the 3 × 3 Matrix That Produces the Described (x,y)→(x+7,y+4)( x , y ) \rightarrow ( x + 7 , y + 4 )(x,y)→(x+7,y+4)

Find the 3 × 3 Matrix That Produces the Described $( x , y ) \rightarrow ( x + 7 , y + 4 )$