Final answer:
The question is about reflecting a triangle over the line y = -x using matrix transformation. The correct matrix for this reflection is [[0, -1], [1, 0]], which swaps and negates the x and y coordinates of a point.
Step-by-step explanation:
The question given is about performing a geometric transformation, specifically a reflection over the line y = -x. The matrix transformation [[0, 7, -1], [0, -3, -4]] seems to be unrelated to the question as the reflection matrix for reflecting over the line y = -x is in fact [[0, -1], [1, 0]]. To reflect a triangle over the line y = -x, you would apply this reflection matrix to each vertex of the triangle.
- Represent each vertex of the triangle as a column vector.
- Multiply the reflection matrix by each vertex vector.
- The resulting vectors will give new positions of the reflected vertices.
The correct reflection matrix will have the effect of interchanging the x and y coordinates and changing their signs, effectively mirroring the triangle across the line y = -x.