1. **Problem statement:** Rotate rhombus ABCD with vertices A(1,0), B(6,-2), C(8,-7), and D(3,-5) by 90° counterclockwise about the origin. 2. **Formula for 90° counterclockwise rotation:** $$ (x,y) \to (-y,x) $$ This means each point's new coordinates are found by swapping $x$ and $y$ and changing the sign of the original $y$. 3. **Apply the rotation to each vertex:** - For A(1,0): $$ A' = (-0,1) = (0,1) $$ - For B(6,-2): $$ B' = (-(-2),6) = (2,6) $$ - For C(8,-7): $$ C' = (-(-7),8) = (7,8) $$ - For D(3,-5): $$ D' = (-(-5),3) = (5,3) $$ 4. **Final rotated vertices:** $$ A'(0,1), B'(2,6), C'(7,8), D'(5,3) $$ These are the coordinates of the rhombus after a 90° counterclockwise rotation about the origin.