Please answer all questions/ procedures As well as this prompt If given two pairs of coordinate points, in words, describe the process step bystep, to determine the equation of the perpendicular bisector.

Investigation 14 There are three fire stations, A, B and C, in a town. The coordinates of the fire stations are A ( 1, 4), B(1, 0) and C(4, 3). In order to improve response times, the township has installed a new centralized fire response system, which allows a dispatcher to send a fire truck from the nearest fire station to the location of the fire. How should the township be divided into regions so that there is one fire station in each region and this fire station is the closest one to each house in the region? Use technology or graph paper to complete the investigation. 1 Plot the fire stations A and B on coordinate axes, either by hand or using a software package. 2 Draw the perpendicular bisector of [ AB ] and gently shade those points nearest to A. How would you divide the township into two regions if fire station C is not yet in operation? 3 Add fire station C to the diagram, then find the equations of the perpendicular bisectors of [ AC] and [ BC] and add these to the diagram. How would you divide the township into three sections when the three fire stations A, B and C are fully operational? 4 The township is relocating fire station D within its territory. Station D will have location [5, 1). Divide the township into four regions for the four fire stations A, B, C and D. 5 Why does adding the fire stations one by one make sense for creating a town map? 6 What is the incremental algorithm