1. The problem involves understanding the reflection of a quadrilateral across the vertical line $x = -2$. 2. The line of reflection is given by $x = -2$. This means every point on the quadrilateral will be reflected such that its distance from the line $x = -2$ is preserved but on the opposite side. 3. The formula for reflecting a point $(x, y)$ across the vertical line $x = a$ is: $$x' = 2a - x, \quad y' = y$$ where $(x', y')$ is the reflected point. 4. Applying this to each vertex of the quadrilateral: - For $(1, -2)$: $$x' = 2(-2) - 1 = -4 - 1 = -5, \quad y' = -2$$ - For $(2, -3)$: $$x' = 2(-2) - 2 = -4 - 2 = -6, \quad y' = -3$$ - For $(3, -5)$: $$x' = 2(-2) - 3 = -4 - 3 = -7, \quad y' = -5$$ - For $(2, -6)$: $$x' = 2(-2) - 2 = -4 - 2 = -6, \quad y' = -6$$ 5. The reflected quadrilateral has vertices at $(-5, -2)$, $(-6, -3)$, $(-7, -5)$, and $(-6, -6)$. 6. This reflection preserves the shape and size of the quadrilateral but flips it over the line $x = -2$. Final answer: The reflected quadrilateral vertices are $$(-5, -2), (-6, -3), (-7, -5), (-6, -6)$$.