1. **State the problem:** Jasmine has a desk represented by rectangle ABCD with vertices A(2,4), B(6,4), C(6,1), and D(2,1). She first translates the desk 3 units left and 2 units down, then rotates it 90° clockwise about the origin. We need to find the coordinates after each transformation. 2. **Translation formula:** To translate a point $(x,y)$ by $h$ units horizontally and $k$ units vertically, use: $$ (x,y) \to (x+h, y+k) $$ Here, $h = -3$ (left) and $k = -2$ (down). 3. **Apply translation to each vertex:** - $A(2,4) \to (2-3, 4-2) = (-1, 2)$ - $B(6,4) \to (6-3, 4-2) = (3, 2)$ - $C(6,1) \to (6-3, 1-2) = (3, -1)$ - $D(2,1) \to (2-3, 1-2) = (-1, -1)$ 4. **Rotation formula:** A 90° clockwise rotation about the origin transforms $(x,y)$ to $(y, -x)$. 5. **Apply rotation to translated points:** - $A'(-1, 2) \to (2, -(-1)) = (2, 1)$ - $B'(3, 2) \to (2, -3) = (2, -3)$ - $C'(3, -1) \to (-1, -3)$ (given) - $D'(-1, -1) \to (-1, 1)$ **Final coordinates after both transformations:** - $A'' = (2, 1)$ - $B'' = (2, -3)$ - $C'' = (-1, -3)$ - $D'' = (-1, 1)$