To determine the transformations that demonstrate the congruence of the triangles, we start by noting the positions and shapes of the triangles in the respective quadrants, specifically focusing on the triangle in quadrant 2 and the triangle in quadrant 1.
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Rotation: To align the triangle in quadrant 2 with the triangle in quadrant 1, we can apply a rotation. The key vertices of the triangle in quadrant 1 are located in quadrant 1 and need to reach the position of the vertices in quadrant 2. A rotation of 90 degrees counterclockwise around a central point (midpoint of a line connecting points of both triangles) should adjust their positions into congruence.
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Translation: After rotating the triangle, we may need to translate it in order to match the vertices precisely. By "translating," we shift the entire triangle from its rotated position to the exact location of the corresponding vertices of the other triangle. The translation vector would need to be established based on the coordinates of a specific vertex from the triangle in quadrant 1 to the corresponding vertex in quadrant 2.
In summary, the two transformations to demonstrate that the triangles are congruent are:
- Rotation of 90 degrees counterclockwise and
- Translation of (2, 1) (e.g., from the centroid of the rotated triangle to the target centroid).
Thus, the final answer is: Rotation of 90 degrees counterclockwise and translation of (2, 1).