1. **Problem statement:** Given the rectangle PQRS with vertices P, Q, R, S, find the image points P', Q', R', S' after the transformation (x, y) \to (2x, y). 2. **Transformation formula:** The transformation doubles the x-coordinate and leaves the y-coordinate unchanged. Mathematically, this is: $$ (x, y) \to (2x, y) $$ 3. **Apply the transformation to each vertex:** - For P, if original coordinates are $(x_P, y_P)$, then $$ P' = (2x_P, y_P) $$ - For Q, similarly, $$ Q' = (2x_Q, y_Q) $$ - For R, $$ R' = (2x_R, y_R) $$ - For S, $$ S' = (2x_S, y_S) $$ 4. **Given transformed points:** - $P' = (-1, 2)$ - $Q' = (4, 2)$ - $R' = (4, -1)$ - $S' = (-4, -1)$ 5. **Find original points by reversing the transformation:** Since $P' = (2x_P, y_P)$, then $$ x_P = \frac{P'_x}{2}, \quad y_P = P'_y $$ Calculate each: - $P = \left(\frac{-1}{2}, 2\right) = (-0.5, 2)$ - $Q = \left(\frac{4}{2}, 2\right) = (2, 2)$ - $R = \left(\frac{4}{2}, -1\right) = (2, -1)$ - $S = \left(\frac{-4}{2}, -1\right) = (-2, -1)$ 6. **Explanation:** The transformation stretches the rectangle horizontally by a factor of 2, doubling the x-coordinates while keeping y-coordinates the same. 7. **Graph description:** The image P'Q'R'S' is a horizontally stretched version of PQRS.