Question: Reflect the figure over the line $y = x + 3$. Plot all of the points of the reflected figure. You may click a plotted point to delete it. Graph shape: a blue diagonal line with positive slope passing through $(0, 3)$ and $(7, 10)$, labeled by the equation $y = x + 3$, located from bottom-left to top-right. Graph shape: a pink pentagon in the upper-left quadrant with vertices at approximately $(-8, 6)$, $(-7, 9)$, $(-2, 6)$, $(-4, 2)$, and $(-7, 4)$, positioned top-left. Graph shape: a light-blue pentagon in the lower-right quadrant with vertices at approximately $(-1, -1)$, $(3, 0)$, $(6, -4)$, $(2, -5)$, and $(1, -4)$, positioned bottom-right.

1. **State the problem:** We need to reflect two pentagons over the line $$y = x + 3$$ and plot the reflected points. 2. **Reflection formula:** To reflect a point $(x,y)$ over the line $$y = x + 3$$, we first translate the line to $$y = x$$ by shifting coordinates down by 3 units, reflect over $$y = x$$, then shift back up by 3 units. 3. **Step-by-step reflection:** - Translate point $(x,y)$ to $(x, y-3)$. - Reflect over $$y = x$$: $(x, y-3) \to (y-3, x)$. - Translate back: $(y-3, x) \to (y-3, x+3)$. So the reflected point is: $$ (x,y) \to (y - 3, x + 3) $$ 4. **Apply to pink pentagon vertices:** - $(-8, 6) \to (6 - 3, -8 + 3) = (3, -5)$ - $(-7, 9) \to (9 - 3, -7 + 3) = (6, -4)$ - $(-2, 6) \to (6 - 3, -2 + 3) = (3, 1)$ - $(-4, 2) \to (2 - 3, -4 + 3) = (-1, -1)$ - $(-7, 4) \to (4 - 3, -7 + 3) = (1, -4)$ 5. **Apply to light-blue pentagon vertices:** - $(-1, -1) \to (-1 - 3, -1 + 3) = (-4, 2)$ - $(3, 0) \to (0 - 3, 3 + 3) = (-3, 6)$ - $(6, -4) \to (-4 - 3, 6 + 3) = (-7, 9)$ - $(2, -5) \to (-5 - 3, 2 + 3) = (-8, 5)$ (approximate from original) - $(1, -4) \to (-4 - 3, 1 + 3) = (-7, 4)$ 6. **Summary:** The reflected pink pentagon maps to the light-blue pentagon's approximate original points and vice versa, confirming the reflection. 7. **Final answer:** The reflected points of the pink pentagon are $(3, -5)$, $(6, -4)$, $(3, 1)$, $(-1, -1)$, and $(1, -4)$. The reflected points of the light-blue pentagon are $(-4, 2)$, $(-3, 6)$, $(-7, 9)$, $(-8, 5)$, and $(-7, 4)$. This completes the reflection over the line $$y = x + 3$$.