Answer:
D. reflection across the line y = -x.
Explanation:
The transformation that did NOT take place is reflection across the line y = -x.
To see this, we can consider the coordinates of the vertices of triangle ABC. Triangle ABC is inscribed in a circle with center A(3, 3), so the coordinates of its vertices must be within a distance of 3 units of A.
If we reflect triangle ABC across the line y = -x, the coordinates of its vertices will be negated. This means that the new triangle, triangle A'B'C', will be inscribed in a circle with center A'(-3, -3), but its vertices will not be within a distance of 3 units of A'.
For example, if one of the vertices of triangle ABC is (2, 1), then its reflection across the line y = -x will be (-2, -1). This point is not within a distance of 3 units of A'(-3, -3).
In contrast, the other three transformations did take place.
Rotation 180° counterclockwise about the origin: This transformation will map triangle ABC to a triangle with the same vertices, but in the opposite orientation. This is consistent with the graph, which shows triangle A'B'C' as a reflection of triangle ABC across the x-axis.
Reflection across the origin: This transformation will map triangle ABC to a triangle with the same vertices, but in the opposite quadrant. This is consistent with the graph, which shows triangle A'B'C' as a reflection of triangle ABC across the origin.
Rotation 180° clockwise about the origin: This transformation will map triangle ABC to a triangle with the same vertices, but in the opposite orientation. This is consistent with the graph, which shows triangle A'B'C' as a reflection of triangle ABC across the y-axis.
Therefore, the answer is D. reflection across the line y = -x.