The only sequence of transformations that maps ABC to A'B'C' is reflecting across the line y = x, followed by translating 4 units down.
The correct sequence of transformations that maps ABC to A'B'C' is:
Step 1: Reflect across the line y = x.
This transformation flips the triangle across the diagonal line, resulting in triangle A'B'C'.
Step 2: Translate 4 units down.
This transformation moves the triangle 4 units вниз without changing its orientation.
Here's why the other options are incorrect:
Rotate 90 degrees clockwise about the origin: This would rotate the triangle clockwise, not diagonally as needed.
Reflect across the y-axis: This would flip the triangle across the vertical axis, resulting in a triangle that is not congruent to A'B'C'.
Reflect across the x-axis: This would flip the triangle across the horizontal axis, resulting in a triangle that is not congruent to A'B'C'.
Translate 1 unit right or 2 units right: These translations would move the triangle to the right, but not downwards as needed.
Translate 3 units up: This translation would move the triangle up, but not downwards as needed.
Therefore, the only sequence of transformations that maps ABC to A'B'C' is reflecting across the line y = x, followed by translating 4 units down.