Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
-Translation by the vector (4, -6, -3)72)
A)
$\left[ \begin{array} { r r r r } 1 & 0 & 0 & 4 \ 0 & 1 & 0 & - 6 \ 0 & 0 & 1 & - 3 \ 0 & 0 & 0 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { r r r r } 1 & 0 & 0 & - 4 \ 0 & 1 & 0 & 6 \ 0 & 0 & 1 & 3 \ 0 & 0 & 0 & 1 \end{array} \right]$

C)
$\left[ \begin{array} { r r r r } 0 & 0 & 0 & 4 \ 0 & 0 & 0 & - 6 \ 0 & 0 & 0 & - 3 \ 0 & 0 & 0 & 1 \end{array} \right]$

D)

$\left[ \begin{array} { r r r r } 4 & 0 & 0 & 0 \ 0 & - 6 & 0 & 0 \ 0 & 0 & - 3 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$

Question

Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
-Translation by the vector (4, -6, -3)72) 
A)
$\left[ \begin{array} { r r r r } 1 & 0 & 0 & 4 \ 0 & 1 & 0 & - 6 \ 0 & 0 & 1 & - 3 \ 0 & 0 & 0 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { r r r r } 1 & 0 & 0 & - 4 \ 0 & 1 & 0 & 6 \ 0 & 0 & 1 & 3 \ 0 & 0 & 0 & 1 \end{array} \right]$

C)
$\left[ \begin{array} { r r r r } 0 & 0 & 0 & 4 \ 0 & 0 & 0 & - 6 \ 0 & 0 & 0 & - 3 \ 0 & 0 & 0 & 1 \end{array} \right]$

D)

$\left[ \begin{array} { r r r r } 4 & 0 & 0 & 0 \ 0 & - 6 & 0 & 0 \ 0 & 0 & - 3 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The correct matrix for a translation by the vector (4, -6, -3) in homogeneous coordinates is the one where the translation components are placed in the last column of the matrix, with the diagonal elements set to 1 to preserve the original coordinates and the last row set to (0, 0, 0, 1) to maintain the homogeneous coordinate system.

Find the 4 × 4 Matrix That Produces the Described [1004010−6001−30001]\left[ \begin{array} { r r r r } 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 6 \\ 0 & 0 & 1 & - 3 \\ 0 & 0 & 0 & 1 \end{array} \right]​1000​0100​0010​4−6−31​​

Find the 4 × 4 Matrix That Produces the Described $\left[ \begin{array} { r r r r } 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & - 6 \\ 0 & 0 & 1 & - 3 \\ 0 & 0 & 0 & 1 \end{array} \right]$