1. **State the problem:** Translate the triangle with vertices A(2,4), B(1,2), C(4,2) by the vector (-4,1). 2. **Write the transformation rule:** The translation rule is given by $$(x, y) \to (x - 4, y + 1)$$ This means each point moves 4 units left and 1 unit up. 3. **Apply the translation to each vertex:** - For A(2,4): $$A' = (2 - 4, 4 + 1) = (-2, 5)$$ - For B(1,2): $$B' = (1 - 4, 2 + 1) = (-3, 3)$$ - For C(4,2): $$C' = (4 - 4, 2 + 1) = (0, 3)$$ 4. **Fill in the table:** | Preimage Coordinates (x, y) | Image Coordinates (x', y') | |-----------------------------|----------------------------| | A (2, 4) | A' (-2, 5) | | B (1, 2) | B' (-3, 3) | | C (4, 2) | C' (0, 3) | 5. **Summary:** The triangle is shifted left by 4 units and up by 1 unit, resulting in the new vertices A'(-2,5), B'(-3,3), and C'(0,3).