1. **State the problem:** We have three points A, B, and C on a grid. The path from A to B is vertical, and the path from B to C is diagonal. The cost per metre of the path is fixed. 2. **Given:** - Cost of path from A to B is 14800. - We need to find the cost of the path from B to C. 3. **Step 1: Find the distance from A to B.** Since the path from A to B is vertical, the distance is the number of vertical squares between A and B. 4. **Step 2: Find the distance from B to C.** The path from B to C is diagonal. We use the distance formula for points on a grid: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 5. **Step 3: Calculate the cost per metre.** Cost per metre = $\frac{\text{Cost from A to B}}{\text{Distance from A to B}}$ 6. **Step 4: Calculate the cost from B to C.** Cost from B to C = (Cost per metre) $\times$ (Distance from B to C) --- **Assuming the grid squares are 1 metre each and from the description:** - Distance A to B = 4 squares (vertical) - Distance B to C: horizontal difference = 5 squares, vertical difference = 4 squares Calculate distance B to C: $$d = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41}$$ Calculate cost per metre: $$\text{Cost per metre} = \frac{14800}{4} = 3700$$ Calculate cost from B to C: $$\text{Cost} = 3700 \times \sqrt{41} \approx 3700 \times 6.4031 = 23691.47$$ Rounded to the nearest pound: **23691** Therefore, the cost of the path between points B and C is approximately 23691.