1. **State the problem:** We need to find the length of the pipe running diagonally from the floor drain at point $(2, 2)$ to the sewer connection at point $(10, 17)$ in a coordinate plane, then calculate the total cost given the price per metre. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate the distance:** $$d = \sqrt{(10 - 2)^2 + (17 - 2)^2} = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289}$$ 4. **Simplify the square root:** $$d = 17 \text{ metres}$$ 5. **Calculate the total cost:** Cost per metre = 3.15 Total cost = $17 \times 3.15 = 53.55$ 6. **Answer:** The builder should budget 53.55 for the pipe.