1. **State the problem:** Determine if rectangle EFGH is a dilation of rectangle ABCD with the center of dilation at the origin (0,0). 2. **List vertices and side lengths:** - ABCD vertices: A(-3,2), B(1,2), C(1,-1), D(-3,-1) - EFGH vertices: E(-4,3), F(2,3), G(2,-2), H(-4,-2) Sides of ABCD: - Length AB = distance between (-3,2) and (1,2) = $$|1 - (-3)| = 4$$ - Length BC = distance between (1,2) and (1,-1) = $$|2 - (-1)| = 3$$ Sides of EFGH: - Length EF = distance between (-4,3) and (2,3) = $$|2 - (-4)| = 6$$ - Length FG = distance between (2,3) and (2,-2) = $$|3 - (-2)| = 5$$ 3. **Check ratio of side lengths:** - Horizontal sides ratio = $$\frac{6}{4} = 1.5$$ - Vertical sides ratio = $$\frac{5}{3} \approx 1.6667$$ Since these ratios are not equal, the scale factor would not be consistent for both dimensions. 4. **Check slopes of corresponding sides:** Both rectangles have sides parallel to the axes (slopes 0 and undefined), so corresponding sides have the same slopes. 5. **Check the position under dilation with center at origin:** - If ABCD was dilated by scale factor $$k$$ from the origin, point A(-3,2) would map to $$(-3k, 2k)$$. - The image of A is E(-4,3). So, $$-3k = -4$$ gives $$k = \frac{4}{3}$$ and $$2k = 3$$ gives $$k = \frac{3}{2}$$. The scale factors from x and y coordinates differ, so E is not a dilation of A with center at origin. **Conclusion:** Rectangle EFGH is not a dilation of ABCD centered at the origin because the scale factors from the origin to corresponding vertices are not equal and side lengths ratios differ. **Final answer:** No, because the center of dilation is not at (0, 0) and corresponding sides do not have consistent scale ratios.