Answer:
The matrix expression that represents the transformation is:
Option: C
![4\cdot \left[\begin{array}{ccc}2&9\\-5&1\\1&-4\end{array}\right]](https://img.qammunity.org/2017/formulas/mathematics/high-school/g74jg8rn18oqwz94lnaatibxmrys4mq92x.png)
Explanation:
We are given a vertices of a triangle as:
(2, 9), (-5, 1), and (1,- 4)
This means that in the matrix representation these vertices could be represented as:
![\left[\begin{array}{ccc}2&9\\-5&1\\1&-4\end{array}\right]](https://img.qammunity.org/2017/formulas/mathematics/high-school/dgis80dlkjqq1c30yd3awe5kks660z8co8.png)
Now, when these vertices are dilated by a scale factor of 4, the change in vertices are:
Each of the vertices are multiplied by 4.
i.e. each of the entry in the matrix is multiplied by 4.
or we can take common 4 from the matrix to obtain the transformed vertices in the form as:
![4\cdot \left[\begin{array}{ccc}2&9\\-5&1\\1&-4\end{array}\right]](https://img.qammunity.org/2017/formulas/mathematics/high-school/g74jg8rn18oqwz94lnaatibxmrys4mq92x.png)