Cellular phone towers in a town are represented bkj/+ f.ppihwja *.0t py the points P, Q, R, and S (not shown) in the partially complete Voronoi diagram shown below. The regions created bwpj. *+kfp. ap/0tjhiy the diagram represent the phone coverage provided by each tower.



1.Write down the coordinates of the missing phone tower S. (a,b) a=   b=  
2.Calculate the coverage area provided by phone tower Q. A =    $km^2$
3.Find the gradient of the edge of Voronoi diagram between towers Q and R. $m_{e,QR}$ =   
The phone towers provide different data download speeds, as per the table below.


Tower is P ;Data download speed is 25 MBps ;Tower is R ;Data download speed is 30 MBps ;Tower is Q & S ;Data download speed is 20 MBps ;
4.A customer is located at (4,10). Determine the download speed she receives.

  Consider the Voronoi diagram belhmm6 d3ab qz89 q96jr 9o3ev b6vyv2laow with sites A, B, C and D, and intersections E zmb md23bv9o663 9lrhaeq ayvj6q8v9and F.



1.Determine the site closest to the coordinate (9,6).
2.Determine the coordinates of the centre of the largest empty circle.
3.Calculate the area of the largest empty circle. a ≈    $units^2$

  Points A(1,5)，B(5,9),C(7,7),D(9,3) and E(13, *o.q6 bh6c0(y z kz:hqbz,bxy11) represent feeding-racks for dears in the Teutoburg Forest qbz* by:,q zkochbyhz.606(x in Germany. The feeding-racks are illustrated in the following coordinate axes.
Horizontal scale: 1 unit represents 1 km.
Vertical scale: 1 unit represents 1 km.

1.Calculate the gradient of the line segment CE.
Three straight lines are drawn on the coordinate axes to form an incomplete Voronoi diagram. $m_{CE}$ = $\frac{a}{b}$ a =    b =   
2.Find the equation of the line that would complete the Voronoi cell containing site C. Give your answer in the form
ax+by+d=0 where a,b,d∈Z. ax+by+c=0 a =    b =    c =   

3.In the context of the question, explain the meaning of the Voronoi cell containing site C.

  Points A(−3,5), B(5,3), C(3,9), D(3,−3) and E(11,5) reprey5 o2 (eflx(ghaj9f2m.p 6me psent coffee shops in a city. The coffee sh5ao.(me96x(f p2hpj2l myfgeops are illustrated on the following coordinate axes.
Horizontal scale: 1 unit represents 1 km.
Vertical scale: 1 unit represents 1 km.



1.Calculate the gradient of the line segment BE.
The diagram below shows three straight lines that form an incomplete Voronoi diagram.



2.Find the equation of the line completing the Voronoi cell containing site B. Give your answer in the form ax+by+d=0 where a,b,d∈Z. ax+by+c=0 a =    b =    c =   
3.In the context of the question, explain the meaning of the Voronoi cell containing site B.

  The Voronoi diagram below shows four hotels in ltbxc0 n 08l v6.4h+ulq w*a fb62czuea small town represented by points with coordinates A(−4,4), B(3,5), C(3,−3), and D(−1,3). The vertices l.vblb0u lewq zt+0f *2cc646hnu 8ax$V_1$​, $V_2$​ and $V_3$​ are also shown. Distances in the direction of the x and y axes are measured in increments of 100 metres.

  Consider the Voronoi diagram below for a city that cont;d0p lxb1v n9pw4v-swsg5n*m ains the towns A, B, C, anvnn*-psdpw ;lmgb 54sw9 0 x1vd D.
The equation of the perpendicular bisector between sites A and D, PB(A,D), is found to be
y=x−25​

1.Determine the equation of the perpendicular bisector between C and D, PB(C,D).y =-$\frac{a}{b}$x+$\frac{c}{d}$ a =    b =    c =    d =   
2.Hence, determine the coordinates of the intersection $V_2$​. (a,b) a=   b=  
3.Determine the optimal position for a toxic waste dump in this city, such that it is as far away from a town as possible.

  Consider the Voronoi diagram below thqk19 o7d:c uchat shows the location of convenient stores within a town. The concc9 ohkdu:q7 1venient stores are labelled A, B, C, and D.
The equation of the perpendicular bisector between sites A and D, PB(A,D), is found to be
y=−x+6​






1.Determine the equation of the perpendicular bisector between sites C and D, PB(C,D).y =$\frac{a}{b}$x-$\frac{c}{d}$ a =    b =    c =    d =   
2.Hence, determine the coordinates of the intersection $V_1$​.
A company that opens and manages convenient stores wants to open a new store in this town. (\frac{a}{b},\frac{c}{d}) a =    b =    c =    d =   
3.Determine the optimal position for this new store, so that it is as far as possible from its nearest store.

  A town currently has four Italian pizza restaurants. A famous ca uuevq ps r8z232 qi z:zqn+d;e1m,*ehef wishes to open a new d2v3qpa :e*+ze 1;z8zsqm qui2,un r epizza restaurant in the town but wants it to be located as far away as possible from the four current restaurants.
The Voronoi diagram below showing the positions of the four current restaurants on a set of coordinates axes: A(2,3) B(8,4), C(7,1), and D(2,1), where one unit represents 1 km.



1.Write down the coordinates of P. (a,b) a=   b=  
2.Show that the coordinates of Q are(5.03,3.32), correct to three significant figures.(a,b) a=   b=  
3.Determine where the famous chef should position their new restaurant.

4.Determine the estimated average weekly number of pizzas this new shop will sell. ≈    pizzas

  The Voronoi diagram below shows the location of fire stations in outbac1hp6l ro*;dh wmib;qub*r:/pd q,gv 2k Queensland, a North-Eastern state of Austravo1qp dumqi*; gr 2h,*rbhbpl ;d6:w/lia.
Horizontal scale: 1 unit represents 100 km.
Vertical scale: 1 unit represents 100 km.



1.Identify the nearest fire-station to houses located at
(1)(300,300)   
(2)(−200,100)   
A house located at (200,200) has an internal fire and requires assistance.
2.Determine which fire-stations the house is closest to.    and   
3.Determine how far the house is from these two fire-stations. Give your answer to the nearest kilometre. d ≈    km

  The Voronoi diagram below shows tcuj3 l t4dfzw l;80aoh8rd*. she location of fire stations in outback Queenslac8 lj. zd4t* dh 38l;uawr0sfond, a North-Eastern state of Australia.
Horizontal scale: 1 unit represents 100 km.
Vertical scale: 1 unit represents 100 km.



1.Identify the nearest fire-station to houses located at
(1)(300,300)   
(2)(−200,100)   
A house located at (200,200) has an internal fire and requires assistance.
2.Determine which fire-stations the house is closest to.    and   
3.Determine how far the house is from these two fire-stations. Give your answer to the nearest kilometre. d ≈    km

  The Voronoi diagram below shows the fitness studios A, B and C, located in a parzy kli.n83f 0:nit(b-e n/0pu:vzkd yticular distriyii :0 ndbe (v0zpkft.8:3 l/nknuy-zct.



1.On the diagram, shade the cell with the missing fitness studio.
2.Determine the coordinates of the missing fitness studio, D.
3.Jennifer lives an equal distance from fitness studios A and D. Find the shortest possible distance Jennifer's house could be from fitness studios A and D. d ≈    km

  The sites A, B (not shown), C, and D in the Voronoi diagram below represenm; 6c mci-(jrq.z cgy4j mm3woa0-i y9t the location of rainfall recording gauges on a large corqi;omm j iwjm-- z( c46ayycr.m93cg0 n farm in Texas, USA.
Horizontal scale: 1 unit represents 1 km.
Vertical scale: 1 unit represents 1 km.

1.Site B is missing from the diagram. Write down its coordinates. B : (a,b) a=   b=  
2.Calculate the area of the cell C. A =    $km^2$
3.Find the distance from point E(9,8) to the nearest rainfall recording gauge.
The table below shows measurements of the average monthly rainfall (mm) of each of the recording gauges. d =    km

4，Estimate the average monthly rainfall at point F(1,6) in mm.    mm