1. **State the problem:** We need to find a series of transformations that map Figure J with vertices approximately at $(-6,7)$, $(-5,3)$, $(-3,2)$, and $(-2,7)$ onto Figure K with vertices approximately at $(3,-3)$, $(4,-6)$, $(7,-7)$, and $(6,-3)$. 2. **Analyze the figures:** Figure J is in the top-left quadrant, and Figure K is in the bottom-right quadrant. The shapes appear congruent but reflected and translated. 3. **Step 1: Reflection** Reflect Figure J across the $y$-axis to move it from the left side to the right side. The reflection formula across the $y$-axis is: $$ (x,y) \to (-x,y) $$ Applying to vertex $(-6,7)$: $$ (-6,7) \to (6,7) $$ Similarly for other vertices. 4. **Step 2: Rotation** Rotate the reflected figure $180^\circ$ about the origin to move it from the top-right quadrant to the bottom-left quadrant. Rotation formula for $180^\circ$ about origin: $$ (x,y) \to (-x,-y) $$ Applying to $(6,7)$: $$ (6,7) \to (-6,-7) $$ 5. **Step 3: Translation** Translate the figure right and up to match Figure K's position. Calculate translation vector by comparing a vertex of the rotated figure to the corresponding vertex of Figure K. For example, from $(-6,-7)$ to $(7,-7)$: Translation vector is: $$ (7 - (-6), -7 - (-7)) = (13,0) $$ Apply translation: $$ (x,y) \to (x+13,y) $$ 6. **Summary of transformations:** - Reflect across the $y$-axis: $(x,y) \to (-x,y)$ - Rotate $180^\circ$ about origin: $(x,y) \to (-x,-y)$ - Translate by $(13,0)$: $(x,y) \to (x+13,y)$ These transformations map Figure J onto Figure K.