1. **State the problem:** We have three congruent rectangles arranged so that each is rotated 90° around a vertex of the previous one. Given points $A(2,5)$ and $B(4,1.5)$, find coordinates of points $C$ and $D$. 2. **Understand the rectangle and rotation:** The vector from $A$ to $B$ is one side of the rectangle. Since rectangles are congruent and rotated 90°, the next side is perpendicular and equal in length. 3. **Calculate vector $\overrightarrow{AB}$:** $$\overrightarrow{AB} = (4-2, 1.5-5) = (2, -3.5)$$ 4. **Length of $\overrightarrow{AB}$:** $$|\overrightarrow{AB}| = \sqrt{2^2 + (-3.5)^2} = \sqrt{4 + 12.25} = \sqrt{16.25}$$ 5. **Find vector $\overrightarrow{BC}$ by rotating $\overrightarrow{AB}$ by 90°:** A 90° rotation of vector $(x,y)$ is $(-y, x)$. $$\overrightarrow{BC} = (-(-3.5), 2) = (3.5, 2)$$ 6. **Calculate coordinates of $C$:** $$C = B + \overrightarrow{BC} = (4 + 3.5, 1.5 + 2) = (7.5, 3.5)$$ 7. **Find vector $\overrightarrow{CD}$ by rotating $\overrightarrow{BC}$ by 90°:** $$\overrightarrow{CD} = (-2, 3.5)$$ 8. **Calculate coordinates of $D$:** $$D = C + \overrightarrow{CD} = (7.5 - 2, 3.5 + 3.5) = (5.5, 7)$$ **Final answer:** $$C = (7.5, 3.5), \quad D = (5.5, 7)$$