Question

which matrix addition represents the geometric transformation of the given polygon 4 units up and 2 units left? 0, 0, 2, 2, -1, -3, 0, -2+-2, -2, -2, -2, 4, 4, 4, 4 0, 0, 2, 2, -1, -3, 0, -2+4, 4, 4, 4, 2, 2, 2, 2 0, 0, 2, 2, -1, -3, 0, -2+4, 4, 4, 4, -2, -2, -2, -2

Explanation:

Step1: Understand the translation rules

In a coordinate - plane, moving a point $(x,y)$ 4 units up and 2 units left means the new coordinates $(x',y')$ are given by $x'=x - 2$ and $y'=y + 4$. For a polygon represented by a matrix of its vertex coordinates, we add the translation values to the corresponding coordinates of each vertex. The $x$ - coordinates of the vertices in the matrix should be added with $- 2$ and the $y$ - coordinates should be added with 4.

Step2: Analyze the matrices

The first matrix represents the original coordinates of the vertices of the polygon. The second matrix should represent the translation values. The correct matrix addition for a translation of 4 units up (add 4 to the $y$ - coordinates) and 2 units left (add - 2 to the $x$ - coordinates) is

$$\begin{bmatrix}0&0&2&2\\-1&-3&0&-2\end{bmatrix}+\begin{bmatrix}-2&-2&-2&-2\\4&4&4&4\end{bmatrix}$$

.

Answer:

$$\begin{bmatrix}0&0&2&2\\-1&-3&0&-2\end{bmatrix}+\begin{bmatrix}-2&-2&-2&-2\\4&4&4&4\end{bmatrix}$$