Question

Reflect the given triangle over the line y = -x with the matrix transformation [[0, 7, -1], [0, -3, -4]].

Answer 1

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.

1. Represent each vertex of the triangle as a column vector.
2. Multiply the reflection matrix by each vertex vector.
3. 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.