1. The problem asks to identify the two transformations that show figure ABCD is congruent to figure A'B'C'D'. 2. Given the coordinates: - ABCD: A(6,6), B(8,6), C(8,2), D(6,2) - A'B'C'D': A'(8,-8), B'(6,-8), C'(6,-4), D'(8,-4) 3. First, observe the reflection. The points of ABCD are reflected over the line $y=-x$ or equivalently reflected across the line $y=-7$ (since the y-coordinates change sign and shift). This flips the rectangle vertically. 4. Next, a translation moves the reflected figure to the new position. The translation vector can be found by comparing a point and its image, for example: $$\text{Translation vector} = (8 - 6, -8 - 6) = (2, -14)$$ 5. Therefore, the two transformations are: - A reflection (flipping the figure over a horizontal line) - A translation (sliding the figure by vector $(2, -14)$) 6. These transformations preserve distances and angles, so figure ABCD is congruent to figure A'B'C'D'. Final statement: A reflection and a translation show figure ABCD is congruent to figure A'B'C'D'.