Break this into parts by figuring the distance between each point then adding them together to get the total. Then apply unit conversion to get the cable length in meters.
Get the delta x and delta y first (change in x-coordinate, change in y coordinate)
AB: delta x = -8 - (-18) = 10, delta y = (1 - 12) = -11
The use pythagorean's theorem: c = sqrt(a^2 + b^2).
length AB = sqrt(10^2 + (-11)^2) = sqrt(221) = 14.86
BC: delta x = (3 - (-8)) = 11, delta y = 4 - 1 = 3
length BC = sqrt(11^2 + 3^2) = sqrt(130) = 11.40
CD: delta x = 15 - 3 = 12, delta y = 7 - 4 = 3
length CD = sqrt(12^2 + 3^2) = sqrt(153) = 12.37
Sum them to get the total units traversed:
AB + BC + CD = 14.86 + 11.40 + 12.37 = 38.63 units
Apply your unit conversion (one unit = 2.5 meters)
cable length = 38.63 units * 2.5 m/unit = 96.575 m
Answer to nearest tenth is 96.6 m
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?
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