1. The problem states that quadrilateral PQRS is dilated by a scale factor of 2 with the center of dilation at the origin. We need to find the coordinates of point S' after dilation. 2. The formula for dilation of a point $(x, y)$ with center at the origin and scale factor $k$ is: $$ S' = (kx, ky) $$ 3. Given point $S$ has coordinates $(-5, 2)$ and the scale factor $k = 2$. 4. Applying the dilation formula: $$ S' = (2 \times (-5), 2 \times 2) $$ 5. Simplifying: $$ S' = (-10, 4) $$ 6. Therefore, the coordinates of point $S'$ after dilation are $(-10, 4)$. This means the point moves twice as far from the origin in the same direction.