The <em>matrix operation</em> is the <em>addition subtraction </em>and <em>multiplication </em>involving matrices. The coordinates of the <em>image </em>can be represented as a matrix obtained from the coordinates of the <em>preimage </em>through matrix operations
The best correct option is<u> option D)</u>,<em> (the y-coordinate for the point (8, -7) is to be replaced with a 7 to give (7, -7) as follows</em>:
![\left[\begin{array}{rrrr}1&0\\0&-1\end{array}\right] \left[\begin{array}{rrrr}9&7&3&2\\-3&-7&-7&-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7D1%260%5C%5C0%26-1%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7D9%267%263%262%5C%5C-3%26-7%26-7%26-5%5Cend%7Barray%7D%5Cright%5D)
The reason the above matrix value for the matrix operation are correct are as follows:
Known parameters:
From the diagram, we have that the <em>coordinates</em> of the vertices of the preimage are;
(2, -5), (3, -7), (9, -3), and (7, -7)
The <em>coordinates </em>of the vertices of the image are;
(2, 5), (3, 7), (9, 3), and (7, 7)
Required:
The matrix operation for the transformation of the preimage points to the image points
Solution:
The transformation from the coordinates of the vertices of primage to the vertices of image involves the change in the sign from negative to positive, of the y-values of the image, which can be obtained by <em>multiplying by</em> (-1)
Therefore, the required matrix operation is presented as follows:
![\mathbf{\left[\begin{array}{rrrr}1&0\\0&-1\end{array}\right] \left[\begin{array}{rrrr}9&7&3&2\\-3&-7&-7&-5\end{array}\right]} =\left[\begin{array}{rrrr}9&7&3&2\\3&7&7&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7D1%260%5C%5C0%26-1%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7D9%267%263%262%5C%5C-3%26-7%26-7%26-5%5Cend%7Barray%7D%5Cright%5D%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7D9%267%263%262%5C%5C3%267%267%265%5Cend%7Barray%7D%5Cright%5D)
Therefore, the <em>best correct</em> option is option D)
Learn more about matrix operations here:
brainly.com/question/17141646
