A coordinate grid is used on the plan of a new housing development. fibre optic cable is being laid with a mico-tunnelling machine. the cable will link points with coordinates A(-18,12), B(-8,1), C(3,4), and D(15,7), in a run beginning at D. if one unit on the grid represents 2.5m, how much cable is required?

To determine the length of cable required, we need to calculate the distance between each consecutive pair of points and sum them up.

First, let's calculate the distance between points D(15,7) and C(3,4):

1. Determine the horizontal distance: (15 - 3) * 2.5 = 12 units
2. Determine the vertical distance: (7 - 4) * 2.5 = 7.5 units
3. Calculate the diagonal distance using the Pythagorean theorem: √(12^2 + 7.5^2) = √(144 + 56.25) = √200.25 = 14.14 units

Next, let's calculate the distance between points C(3,4) and B(-8,1):

1. Determine the horizontal distance: (3 - (-8)) * 2.5 = 27.5 units
2. Determine the vertical distance: (4 - 1) * 2.5 = 7.5 units
3. Calculate the diagonal distance: √(27.5^2 + 7.5^2) = √(756.25 + 56.25) = √812.5 = 28.5 units

Now, let's calculate the distance between points B(-8,1) and A(-18,12):

1. Determine the horizontal distance: (-8 - (-18)) * 2.5 = 25 units
2. Determine the vertical distance: (1 - 12) * 2.5 = -27.5 units (Note: The negative sign indicates the direction)
3. Calculate the diagonal distance: √(25^2 + (-27.5)^2) = √(625 + 756.25) = √1381.25 = 37.17 units

Finally, we sum up the distances:

14.14 units + 28.5 units + 37.17 units = 79.81 units

Therefore, approximately 79.81 units of cable are required.