The matrix operation is the addition subtraction and multiplication involving matrices. The coordinates of the image can be represented as a matrix obtained from the coordinates of the preimage through matrix operations
The best correct option is option D), (the y-coordinate for the point (8, -7) is to be replaced with a 7 to give (7, -7) as follows:
[tex]\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][/tex]
The reason the above matrix value for the matrix operation are correct are as follows:
Known parameters:
From the diagram, we have that the coordinates of the vertices of the preimage are;
(2, -5), (3, -7), (9, -3), and (7, -7)
The coordinates 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 multiplying by (-1)
Therefore, the required matrix operation is presented as follows:
[tex]\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][/tex]
Therefore, the best correct option is option D)
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