1. The problem states that the figure is dilated by a factor of 2 centered at the origin. This means each point of the figure will be moved away from the origin by twice its original distance. 2. The dilation formula for a point $(x,y)$ with center at the origin and scale factor $k$ is: $$ (x', y') = (kx, ky) $$ 3. Applying the dilation factor $k=2$ to each point: - For $R(-4,1)$: $$R' = (2 \times -4, 2 \times 1) = (-8, 2)$$ - For $Q(2,2)$: $$Q' = (2 \times 2, 2 \times 2) = (4, 4)$$ - For $P(2,0)$: $$P' = (2 \times 2, 2 \times 0) = (4, 0)$$ - For $O(3,-1)$: $$O' = (2 \times 3, 2 \times -1) = (6, -2)$$ - For $N(-1,-1)$: $$N' = (2 \times -1, 2 \times -1) = (-2, -2)$$ 4. The new polygon after dilation is formed by connecting points $R'(-8,2)$, $Q'(4,4)$, $P'(4,0)$, $O'(6,-2)$, $N'(-2,-2)$, and back to $R'(-8,2)$. 5. This dilation doubles the size of the figure while keeping its shape and orientation, centered at the origin. Final answer: The dilated image has vertices at $$(-8,2), (4,4), (4,0), (6,-2), (-2,-2)$$ connected in that order.